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Research Article

A fuzzy description logic based IoT framework: Formal verification and end user programming

Contributed equally to this work with: Miguel Pérez-Gaspar, Javier Gomez, Everardo Bárcenas, Francisco Garcia

Roles Conceptualization, Formal analysis, Investigation, Software, Writing – original draft, Writing – review & editing

Affiliation Department of Telecommunications, National Autonomous University of Mexico, Mexico City, Mexico

Roles Conceptualization, Formal analysis, Investigation, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliation Department of Computer Engineering, National Autonomous University of Mexico, Mexico City, Mexico

• Miguel Pérez-Gaspar, 
• Javier Gomez, 
• Everardo Bárcenas, 
• Francisco Garcia

• Published: March 22, 2024
• https://doi.org/10.1371/journal.pone.0296655
• Peer Review
• Reader Comments

The Internet of Things (IoT) has become one of the most popular technologies in recent years. Advances in computing capabilities, hardware accessibility, and wireless connectivity make possible communication between people, processes, and devices for all kinds of applications and industries. However, the deployment of this technology is confined almost entirely to tech companies, leaving end users with only access to specific functionalities. This paper presents a framework that allows users with no technical knowledge to build their own IoT applications according to their needs. To this end, a framework consisting of two building blocks is presented. A friendly interface block lets users tell the system what to do using simple operating rules such as “if the temperature is cold, turn on the heater.” On the other hand, a fuzzy logic reasoner block built by experts translates the ambiguity of human language to specific actions to the actuators, such as “call the police.” The proposed system can also detect and inform the user if the inserted rules have inconsistencies in real time. Moreover, a formal model is introduced, based on fuzzy description logic, for the consistency of IoT systems. Finally, this paper presents various experiments using a fuzzy logic reasoner to show the viability of the proposed framework using a smart-home IoT security system as an example.

Citation: Pérez-Gaspar M, Gomez J, Bárcenas E, Garcia F (2024) A fuzzy description logic based IoT framework: Formal verification and end user programming. PLoS ONE 19(3): e0296655. https://doi.org/10.1371/journal.pone.0296655

Editor: Nadeem Sarwar, Bahria University - Lahore Campus, PAKISTAN

Received: August 14, 2023; Accepted: December 15, 2023; Published: March 22, 2024

Copyright: © 2024 Pérez-Gaspar et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: Data for experiments: https://kaggle.com/datasets/e9899e7c8b983b13c584b3e7a015b6b7e6f698da6fae8016e5ee21ff3d1086de .

Funding: JG, EB, FG: IA104122, IA105420, IA102822; UNAM-PAPIIT program. JG: 0320403; Ciencia de Frontera CONAHCyT. MPG: Estancia-Posdoctoral; UNAM-DGAPA program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

The Internet of Things (IoT) makes possible communications between people and objects by taking advantage of computing capabilities and hardware accessibility for all types of applications. As a general definition, IoT can be described as an interconnection of many objects through a network that continuously generates information about the physical world. These objects can communicate and be controlled by various agents (other systems or people) to interact and take control of the physical world to manage many services of daily use [ 1 ].

IoT devices can generally be classified into controller boards with microprocessors or micro-controllers, sensors that sense data from the physical world, and actuators that connect to controllers and communication modules. However, the development and deployment of IoT applications are confined almost entirely to tech companies, leaving end users with only access to specific functionalities. This approach presents a fundamental problem since it is only possible for the IoT provider to anticipate some of the user’s needs. Unfortunately, it will take a long time before changes are made to an IoT system to fulfill a user’s specific needs. In this work, we argue that for IoT systems to close the gap between users and IoT technology, a different approach is needed where end users have the means to build their IoT systems according to their specific needs. However, for this end, the interface should be user-friendly, using day-to-day instructions as input, such as “If these conditions happened, then do this or that.” Nevertheless, the system should allow users to express complex system behaviors while at the same time verifying that no inconsistencies appear when additional rules are added.

This work proposes that Fuzzy logic (FL) [ 2 ] is ideally suited to become the interface between people and objects in IoT systems, modeling logical reasoning with vague or ambiguous statements such as “The temperature is hot (cold or mild).” This logic refers to a family of many-valued logic in which truth values are interpreted as degrees of truth. The truth value of a logically complex proposition such as “Carl is tall, and Chris is rich” is determined by the truth values of its constituents. In other words, truth functions impose on classical logic. This type of logic arises from the need to use daily life statements whose natural language adjectives are used to qualify.

Fuzzy logic has been applied in various ways in sensor networks and IoT, such as energy savings, packet routing, location, and human-sensor interface, among other applications [ 3 – 6 ]. An advantage of fuzzy logic over traditional logic is that the former can reach precise conclusions based on vague, imprecise, noisy, or non-existent arguments common in IoT systems since messages are often lost, collected information is imprecise, or the instructions are vague [ 7 ]. Moreover, many IoT applications require human intervention where the user might provide ambiguous inputs to the system, such as higher, smaller, or bigger, that an actuator cannot read directly.

Fig 1 illustrates the flow diagram of the proposed framework. First, a technician (or even the user) needs to place and connect various sensors and actuators that compose the IoT hardware on which the IoT system operates. Some important contextual concepts may be pre-programmed onto the system, such as really hot and air conditioning set to high. Nevertheless, users may modify these concepts later on. The input is given by simple everyday rules such as instructions 1 and 2 , then a fuzzy reasoner will process the user’s input. If the last instruction contradicts another previous rule, the system will alert the user accordingly. Once the system is programmed with non-contradictory (consistent) instructions, it routinely performs its corresponding tasks (e.g., turn on the heater, set the alarm, etc).

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https://doi.org/10.1371/journal.pone.0296655.g001

The structure of this work is organized as follows: In the first section, we discuss previous research to provide context for our study. Then, in the IoT Systems section, we define the system and introduce the concept of consistency. Next, in the Fuzzy Description Logic Verification section, we explain the basics of fuzzy logic and present a result that shows how consistency relates to both the IoT system and fuzzy description logic. Ultimately, in the Fuzzy Control for an IoT Security System section, we outline the following steps: providing context, setting system rules, and putting the system into action. Finally, we present the program’s syntax and share the experiments we conducted to support and illustrate the concepts we have discussed.

Related work

Fuzzy logic has been used in a wide variety of systems such as the automatic focus of digital cameras [ 10 ], control and optimization of industrial processes and systems [ 11 ], improving the efficiency of fuel-running engines [ 12 ], environmental improvement [ 13 ], expert systems [ 14 ], robotics [ 15 ], vehicles and autonomous driving [ 16 ], computer technology [ 17 ], Fuzzy databases [ 18 ], artificial intelligence, control systems for air conditioners [ 19 ], family appliances [ 3 , 20 ], wireless sensor networks [ 3 – 6 ], and cellular automata [ 21 – 23 ].

Concerning formal verification of IoT systems, the authors in survey [ 24 ] present various works focused on verifying security properties [ 25 – 27 ]. Some other IoT works studied the settings of formal verification, including communication protocols [ 28 ], healthcare and environmental monitoring systems [ 29 , 30 ]. Even when all these approaches focus on verifying data, protocols, and security consistency, these proposals work over static variables. On the contrary, the proposal presented in this paper can modify the system’s behavior by adding new rules on running time while the system verifies consistency. Furthermore, none of the above proposals interact with end users.

Input data in IoT systems is usually collected from heterogeneous sensor devices that need more interoperability since data values are based on proprietary formats. Similarly, IoT systems can accumulate poor-quality data since events such as offset data, missing data, wrong time stamps, and wrong attribute values can occur. Verifying the consistency of collected data has traditionally used machine learning and point-based calibration algorithms. For instance, authors in [ 31 ] proposed a data consistency method based on neural networks to reduce data errors by approximately 4%. However, this approach cannot interact in real-time with end users since it verifies consistency before the system starts.

Logical data inconsistencies have also been studied in the description logic (DLs) setting comprising a family of knowledge representation languages [ 32 ]. The balance between computational complexity and the expressiveness of DLs has allowed efficient reasoning tools to be constructed. These tools have enabled the application of DLs in several domains successfully [ 33 ]. Notably, the Web Ontology Language (OWL), a standard for Web Semantics technologies, is based on DLs [ 34 ]. Fuzzy extensions of DLs have also been developed [ 35 ]. These extensions have found application in human activity modeling for ambient intelligence systems [ 36 ], diabetes diagnosis systems [ 37 ], and database systems [ 38 ], to mention a few. Authors in [ 9 ] proposed a consistency data representation for IoT healthcare systems, transforming health data obtained from heterogeneous IoT devices into a semantic data model that supports logical reasoning using OWL. Even when the authors used a logic reasoner, they only focused on creating a unified static data model in which new rules cannot be introduced on running time. In [ 8 ], the authors proposed a reasoning framework to guarantee the consistency of the data stream produced by physical sensors in smart spaces. However, this framework does not interact with end users.

In summary, the proposed framework sets apart from previous works in the literature in two directions, mainly in the context of IoT applications. Firstly, it separates which tasks in the IoT system belong to an expert and which ones are the end user’s responsibility, thus freeing end users from dealing with the most complex part of building and operating an IoT system. Most related works do not make this task distinction, providing little freedom to users wanting to implement their own IoT applications. However, the interaction of expert and user-related tasks will likely generate inconsistencies in the instructions introduced by end users and the data being collected and processed by sensors and actuators. Secondly, this framework verifies the dynamic properties of these task interactions and detects inconsistencies resulting from end-user instructions and wrong data that can be detected in real-time. This may allow end users to identify contradictory instructions so they can be modified to guarantee the IoT system’s correctness. About this point, most related works dealing with consistency focus on verifying static properties defined for the design of the IoT system only, but they do not consider the dynamic aspect once the system is running.

IoT systems

Before providing semantics for IoT System expression, we must precisely define when a sensor or actuator is set to a particular interval domain. This is not immediate since intervals may intersect; for instance, this might be the case for medium and low intervals for a sound sensor. We then introduce the fuzzy membership function m f : D ↦ [0, 1], provided a fuzzy domain D . Fuzzy membership functions may be defined according to the application context of the IoT System. Some standard Fuzzy membership functions are (a) trapezoidal, (b) triangle, (c) rectangular, (d) right-shoulder, and (e) left-shoulder as depicted in Fig 2 .

https://doi.org/10.1371/journal.pone.0296655.g002

Recall the example of the sound sensor intervals intersecting: if the sensed value falls within this intersection, our system employs a special structure to determine which interval is closer to the sensed value.

We are now ready to provide precise semantics of an IoT System. The interpretation of an IoT system rule concerning a Boolean structure B is then defined as follows:

• ⟦ f z ( e ) ∈ d ⟧ B = 1, if and only if, B ( f z ( e ) ∈ d ) = 1;
• ⟦ f z ( e ) ∉ d ⟧ B = 1, if and only if, B ( f z ( e ) ∈ d ) = 0;
• ⟦SystExp 1 ∨ SystExp 2 ⟧ B = 1, if and only if, ⟦SystExp i ⟧ B = 1 for some i ∈ {1, 2};
• ⟦SystExp 1 ∧ SystExp 2 ⟧ B = 1, if and only if, ⟦SystExp i ⟧ B = 1 for all i ∈ {1, 2};
• ⟦If SystExp then f z ( a ) ∈ d ⟧ B = 1, if and only if, ⟦SystExp⟧ B = 0 or ⟦ f z ( a ) ∈ d ⟧ B = 1.

The intuition of interpreting a system rule is that Boolean structures provide a particular context for sensors and actuators.

Definition 2 (IoT System Consistency). We say an IoT System is consistent, if and only if, for all rules of the system R and any Boolean structure B , have that ⟦ R ⟧ B = 1.

Then the system is inconsistent, as there is a Boolean structure considering sensors detecting some movement, low light, and sound, and setting the alarm to medium, such that the interpretation of rule 5 is 0. Note that there is another structure considering the alarm set to low, which causes rule 5 to hold. However, under this structure, rule 4 does not.

Fuzzy description logic verification

In this Section, we describe a fuzzy description logic. Description logics form a family of Knowledge Representation languages, vastly and successfully known among several other domains in the Semantic Web community. The description logic language described in this work allows us to model IoT expert systems in the form of Knowledge Bases (KB). The fuzzy part of language allows us to model ambiguous notions such as “much movement”. We will first describe the syntax and semantics of the logic. Then, the notion of KB consistency is introduced. We next show that the consistency of IoT systems can be tested in terms of KB consistency.

In the setting of an IoT system, the information commonly provided by an expert, such as fuzzy interval for sensor and actuator (much movement, low light, etc.) is described as an ABox. Whereas the information corresponding to rules (instructions) provided by the end user are codified in terms of TBox expressions.

We now introduce the semantic notions of the fuzzy description logic.

• To each modifier m the modifier function f m : [0, 1] D → [0, 1] D .

• To each concrete individual v an element in Δ D .

Definition 8 . Let (⋅)* : SystExp → FDL be a star-interpretation from SystExp(system expressions) to FDL (fuzzy description logic) defined as:

• ( f z ( a ) ∈ d )* = ∃ A . D
• ( f z ( a ) ∉ d )* = ¬(∃ A . D )
• (SystExp 1 ∧ SystExp 2 )* = (SystExp 1 )* ⊓ (SystExp 2 )*
• (SystExp 1 ∨ SystExp 2 )* = (SystExp 1 )* ⊔ (SystExp 2 )*
• (If SystExp then f z ( a ) ∈ d )* = (SystExp)* → (∃ A . D )

We now state the main formal result of the article: IoT system consistency can be tested in terms of Knowledge Base consistency. In practice, consistency is tested before the execution of the IoT system. The following Theorem provides a mathematical guarantee that the system is free of inconsistencies under any real-time scenario (any sensor inputs).

Suppose that the IoT system R 1 , R 2 is consistent, where R 1 is as in the previous step and R 2 = If R 1 then A .

Once the IoT system consistency is verified in terms of Knowledge Base consistency, the system can be executed with the guarantee that no errors can be computed, no matter the inputs from sensors. Values for actuators can be computed from the instructions in the Knowledge Base by means of a defuzzification process. Defuzzification is the output value for the membership function m on the values of the variables in x using the specified defuzzification method. Some examples of defuzzification methods can be seen in the following definition.

Definition 9 . Let B be a fuzzy set to be defuzzified, and let x be an arbitrary element of the universe. Then for all x :

• x LOM is the largest of maxima ( LOM ), if and only if, μ β ( x LOM ) ≥ μ β ( x ), and if μ β ( x LOM ) = μ β ( x ) then x LOM > x .
• x SOM is the smallest of maxima ( SOM ), if and only if, μ β ( x SOM ) ≥ μ β ( x ), and if μ β ( x SOM ) = μ β ( x ) then x SOM < x .

Consider for instance, in the following axiom: (∃move.SomeMove⊓∃light.LowLight⊓∃sound.FewSound) → ∃alarm.MediumAlarm. If input sensors for movement, light, and sound correspond to some, low, and few, respectively, then the alarm should be set to medium. The numerical value corresponding to medium is computed by the defuzzification process.

Fuzzy control for an IoT security system

Smart-home systems are challenging when implementing security systems since wireless sensor devices used in IoT can be heterogeneous and use various communication protocols having different coverage areas when detecting intruders or risk situations. Moreover, even when intelligent IoT devices can monitor their sensors to notify users about potential issues or risks in smart homes, most applications operate without knowledge-based consistency, provoking the system to take wrong actions or presenting failures since more than one rule can contradict each other. For instance, suppose a smart-security home application with sensors that measure light, movement, and sound, and a user is looking for security against an intruder. This system, guided by (a) blueprint, strategically places sensors in the (b) hall, (c) dining room, (d) library, and (e) living room (see small black sensors placed on the walls in Fig 3 ). The goal is to create a secure and comfortable (f) Home (refer to its configuration). A fuzzyDL reasoner is a system in which a user establishes the rules to take actions, for example, calling the police, sending a notification message, or turning on the alarm.

https://doi.org/10.1371/journal.pone.0296655.g003

Let us assume that an expert in security systems has pre-programmed the IoT System with certain restrictions on the RBox, TBox, and Datatypes (Step 1). Since the user can define the TBox with basic rules according to their preferences (Step 2), the objective of the fuzzyDL tool is to verify that the TBox rules are consistent. At the same time, the actuators operate according to the rules established by the user (Step 3). This process involves checking the program syntax and conducting experiments (Program syntax, Experiments) to ensure the smooth running of the system.

Step 1. Contextual information

An expert plays a crucial role by providing specifications regarding the specific context in which IoT systems are implemented. For instance, in the case of a smart home security system, this step meticulously defines what constitutes “high movement” in terms of the numerical data obtained from sensors. Notably, certain information of this nature can be influenced by user preferences, enabling users to modify pre-programmed contextual details. For instance, the interpretation of “hot temperature” might vary between Nordic users and their tropical counterparts. Additionally, finer details, such as the characteristics of fuzzy membership functions (triangular, left shoulder, etc.), are also meticulously delineated in this phase. These precise definitions correspond to the ABox in the corresponding Fuzzy Description Logic Knowledge Base.

The heart of the system lies in its user-friendly interface, designed to gather contextual information effortlessly. This interface adeptly processes natural language instructions through voice or text. To enrich the user experience further, the interface portrays information about sensor types, actuators, and domain values.

Simultaneously, the role of the expert encompasses determining the behavior of sensors and actuators alongside furnishing initial programming for the system. An inherent assumption in this context is the consistency of rules established by the expert. As for system sensors, this illustrative example features three input systems meticulously defined by the expert: light, movement, and sound. These inputs collaboratively contribute to the computation of an output value, which subsequently triggers alert mechanisms.

System sensors. The system, in this instance, encompasses three input systems meticulously outlined by the expert: light, movement, and sound. These inputs harmoniously collaborate to calculate an output value that triggers alert mechanisms.

• Light is associated with three labels: low, medium, and high. For example, LowLight, the label of low light, can be defined as a triangular membership function ( q 1 , q 2 , q 3 ).
• Movement has five labels: low, middle, high, and very high. For example, LowMovement, the label representing low movement, can be defined as a triangular membership function ( q 1 , q 2 , q 3 ).
• sound has five labels: low, middle, high, and very high. For example, LowSound, the label of low sound, can be defined as a triangular membership function ( q 1 , q 2 , q 3 ).

Actuator system. Four actuators were designated with different colors: Green, Yellow, Orange, and Red. For instance, each color corresponds to a specific action, making it a clearer and more precise description of the color-to-action assignment.

• Green: everything is in order.
• Yellow: sending an alert to a cell phone.
• Orange: sending an alert to the police.
• Red: taking further action.

Step 2. System rules

The system’s rules may be pre-programmed, but ideally, non-expert users are expected to define particular rules for the system. Considering the smart home security system, examples are: if movement, light, and sound are low, then do nothing; or if movement, light, and sound are high, then call the police. These instructions correspond to the TBox of the corresponding Fuzzy Description Logic Knowledge Base. A user-friendly interface is also considered for this step: voice or text instructions directly from the users, and information about the system (sensors, actuators, etc.) are depicted to help users define these instructions. At this step, a logic reasoner analyzes the instructions to detect inconsistencies: if the user provides an instruction contradicting an already loaded instruction, the interface provides a warning. In other words, the logic reasoner guarantees that the rules the user introduces are consistent under any system setting. On the other hand, the user’s role is to indicate the rules (the TBox) that satisfy an ideal security system. Furthermore, the consideration of system rules. The number of permutations determined by the labels of each sensor corresponds to the following arithmetic operation 3 × 4 × 4 (for the previous example). Therefore, the system rule-set is 48 rules. Let us assume that the user determined the following four rules:

• R1. IF light IS low AND movement IS low AND sound IS low, THEN code AlertGreen.
• R2. IF light IS low AND movement IS low AND sound IS middle, THEN code AlertYellow.
• R3. IF light IS low AND movement IS low AND sound IS high, THEN code AlertOrange.
• R4. IF light IS low AND movement IS low AND sound IS very-high, THEN code AlertRed.

The interfaces for step 1 (Contextual information) and step 2 (System rule) can be seen in Fig 4 , with (a) representing the expert interface and (b) representing the user interface.

https://doi.org/10.1371/journal.pone.0296655.g004

Step 3. Running the system

Once the contextual information and consistent system rules are defined, then the system is executed. The logical reasoner fuzzyDL consists of three steps: (a) Fuzzification: The numeric inputs (light, movement, sound, light change, movement change, sound change) will be translated into linguistic values (fuzzy sets). (b) Fuzzy inference: Fuzzy rules will be applied to determine how much adjustment is necessary for the security system. (c) Defuzzification: This converts fuzzy outputs obtained from the inference step (Step 2) into a crisp or numerical value. In other words, it transforms the fuzzy sets and their degrees of membership into a single numerical result that represents the system’s output or action. The fuzzy results obtained from the inference step are translated into a numerical action to adjust the security system. One common approach for defuzzification is the MOM method. Finally, when the sensors’ current light, motion, and sound are input into the system, the fuzzy rules will be applied, and the defuzzification will provide a numerical value indicating the action the actuator will follow for the optimum security system.

Program syntax

The internal architecture of the code of our security system programmed in fuzzyDL reasoner is the following:

• System sensors. For each system variable (sensor), we define some specific characteristics that represent it. We also specify its range as a closed subset of the real ones [ k 1 , k 2 ], for example: (functional sensor-1) (functional sensor-2) (functional code) (range sensor-1 *real* k 1 k 2 ) (range sensor-2 *real* k 3 k 4 ) (range code *real* k 5 k 6 ) We define the linguistic labels to describe the value of these variables (using the triangular membership function, see Fig 5 ), such as: For sensor-1 : (define-fuzzy-concept label1 triangular( k 1 k 2 q 1 q 2 q 3 )) (define-fuzzy-concept label2 triangular( k 1 k 2 q 4 q 5 q 6 )) For sensor-2 : (define-fuzzy-concept label1 triangular( k 3 k 4 q 1 q 2 q 3 )) (define-fuzzy-concept label2 triangular( k 3 k 4 q 4 q 5 q 6 ))
• Actuator system. We define linguistic labels to describe the value of actuators. For actuator-1 : (define-fuzzy-concept label1 triangular( k 1 k 2 q 1 q 2 q 3 )) For example, AlertGreen, the label representing that the actuator green is in order, can be defined as triangular ( q 1 , q 2 , q 3 ). We represent the system input as fuzzy statements involving a single digest. (instance individual (= sensor-1 q ′) α ), where q ′ ∈ [ k 1 , k 2 ] (instance individual (= sensor-2 q ″) β ) where q ″ ∈ [ k 1 , k 2 ]
• System rules. The system defines each concept from the rules given by the user, for example: R1. (define-concept Rule1(g-and(some sensor-1 label1)(some sensor-2 label2))) R2. (define-concept Rule2(g-and(some sensor-1 label1)(some sensor-2 label2))) RuleMamd. (define-concept Mamd (g-or Rule1 Rule2))
• Defuzzification. The output of the system is resolved through the use of queries. (defuzzify-mom? Mamd individual sensor-3) (sat RuleMamd)

https://doi.org/10.1371/journal.pone.0296655.g005

The complete internal algorithm of the security system is depicted in Fig 6 .

https://doi.org/10.1371/journal.pone.0296655.g006

Experiments

We conducted a comprehensive analysis of defuzzification and consistency within our security system. In Experiment one (see Table 1 ), we carried out the following tasks:

• Introducing three distinct inputs for light, movement, and sound within the range defined by the expert. We then evaluated the defuzzification ( MOM ) and consistency ( sat ) queries. The outcomes aligned with our expectations.
• For the fourth set of inputs for light, movement, and sound, we deliberately exceeded the predefined range, resulting in an inconsistency flagged by the sat query.
• Lastly, we introduced an additional rule aimed at creating a contradiction within the system, which also resulted in inconsistency as indicated by the sat query.
• Additionally, it is worth noting that the execution times in these experiments exhibited variability. This variability can be attributed to the specific configurations tested, particularly the introduction of contradictory rules that could either halt or significantly extend the program’s execution. These time discrepancies underscore the influence of experimental factors on the system’s performance.

https://doi.org/10.1371/journal.pone.0296655.t001

Finally, in Experiment two (see Table 2 ), we programmed the three rules outlined in the IoT system section. In the program syntax, R2, R4, and R6 correspond to Eqs 3 , 4 and 5 , respectively. Our findings are as follows:

• The (sat) query for rules R2 and R4 yielded a consistent outcome.
• However, the (sat) query involving rules R2, R4, and R6 yielded inconsistency, primarily due to a contradiction between R4 and R6.
• Additionally, the execution times in Experiment two exhibited variation. Notably, The execution of rule R7 showed consistency within 3 seconds. However, when involving rules R8, the program’s execution time was extended to 10 minutes, reflecting inconsistency primarily caused by the interaction between rules R4 and R6.

https://doi.org/10.1371/journal.pone.0296655.t002

The initial and final times were programmed on a computer with the following specifications: Computer Model: [Compaq nc6400]. Processor: [Genuine Intel(R) CPU T2300 1.66Ghz]. RAM: [2.50 GB]. Operating System: [Windows 7 Home Premium].

The conclusions drawn from the analysis presented in the preceding sections fall into two main categories: Fuzzy Logic and IoT systems. First, we derived a theorem that establishes a relationship between the consistency of Fuzzy Logic and IoT systems, specifically in the context of the FuzzyDL reasoner. Second, we developed an algorithm for a security system that employs fuzzy logic as its primary language and identifies inconsistencies between rules. This system can find practical applications in smart homes, however, many other systems can be applied.

Our experiments with the fuzzyDL reasoner provide compelling evidence that the algorithm functions correctly according to the defined problem, even as more rules are added to the system. As an additional step towards the validation and applicability of our system, we plan to conduct evaluations in real-world scenarios. This will involve implementing our system in smart home environments and collecting real-world usage data. By doing so, we will be able to measure the performance and effectiveness of our system in real-world situations and fine-tune it as needed. This real-world evaluation will also allow us to gather feedback from end users, helping us further tailor the system to meet their needs and ensure practical utility. Additionally, we are open to collaborations with the research community and industry to test and validate our system in various applications and scenarios. These additional steps will strengthen our research’s practicality and real-world relevance while fostering collaboration and external validation.

In future work, we plan to explore how the methodology presented in this study can be applied to other IoT systems with varying logic types. Furthermore, we intend to enhance the user interface based on feedback from non-technical users and implement security measures to prevent unintended consequences resulting from user-defined rules.

The system is currently in a prototype stage. The main scalability challenge relies on the fuzzy logic reasoner tool. Other research perspectives include developing and optimizing reasoning algorithms for fuzzy description logic. Similarly, the accuracy of translating natural language instructions into fuzzy logic formulae depends on the accuracy of the corresponding NLP algorithms. We also want to develop NLP interfaces for the proposed frameworks using large language models.

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Fuzzy Logic in Medicine and Bioinformatics

Angela torres.

1 Departamento de Psiquiatría, Radiología y Salud Pública, Facultad de Medicina, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain

Juan J. Nieto

2 Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions) and in bioinformatics (comparison of genomes).

INTRODUCTION

The diagnosis of disease involves several levels of uncertainty and imprecision, and it is inherent to medicine.

A single disease may manifest itself quite differently, depending on the patient, and with different intensities. A single symptom may correspond to different diseases. On the other hand, several diseases present in a patient may interact and interfere with the usual description of any of the diseases.

The best and most precise description of disease entities uses linguistic terms that are also imprecise and vague. Moreover, the classical concepts of health and disease are mutually exclusive and opposite. However, some recent approaches consider both concepts as complementary processes in the same continuum [ 1 – 6 ]. According to the definition issued by the World Health Organization (WHO), health is a state of complete physical, mental, and social well-being, and not merely the absence of disease or infirmity . The loss of health can be seen in its three forms: disease, illness, and sickness.

To deal with imprecision and uncertainty, we have at our disposal fuzzy logic. Fuzzy logic introduces partial truth values, between true and false .

According to Aristotelian logic, for a given proposition or state we only have two logical values: true-false, black-white, 1-0. In real life, things are not either black or white, but most of the times are grey. Thus, in many practical situations, it is convenient to consider intermediate logical values. Let us show this with a very simple medical example. Consider the statement “you are healthy”. Is it true if you have only a broken nail? Is it false if you have a terminal cancer? Everybody is healthy to some degree h and ill to some degree i . If you are totally healthy, then of course h = 1, i = 0. Usually, everybody has some minor health problems and h < 1, but

In the other extreme situation, h = 0 , and i = 1 so that you are not healthy at all (you are dead). In the case you have only a broken nail, we may write h = 0.999, i = 0.001; if you have a painful gastric ulcer, i = 0.6, h = 0.4, but in the case you have a terminal cancer, probably i = 0.95, h = 0.05. As we will see, this is a particular case of Kosko's hypercube: the one-dimensional case [ 4 ].

Uncertainty is now considered essential to science and fuzzy logic is a way to model and deal with it using natural language. We can say that fuzzy logic is a qualitative computational approach.

Since uncertainty is inherent in fields such as medicine and massive data in bioinformatics, and fuzzy logic takes into account such uncertainty, fuzzy set theory can be considered as a suitable formalism to deal with the imprecision intrinsic to many biomedical and bioinformatics problems. Fuzzy logic is a method to render precise what is imprecise in the world of medicine. Several examples and illustrations are mentioned below.

FUZZY LOGIC IN MEDICINE

The complexity of medical practice makes traditional quantitative approaches of analysis inappropriate. In medicine, the lack of information, and its imprecision, and, many times, contradictory nature are common facts. The sources of uncertainty can be classified as follows [ 7 ].

• Information about the patient.
• Medical history of the patient, which is usually supplied by the patient and/or his/her family. This is usually highly subjective and imprecise.
• Physical examination. The physician usually obtains objective data, but in some cases the boundary between normal and pathological status is not sharp.
• Results of laboratory and other diagnostic tests, but they are also subject to some mistakes, and even to improper behavior of the patient prior to the examination.
• The patient may include simulated, exaggerated, understated symptoms, or may even fail to mention some of them.
• We stress the paradox of the growing number of mental disorders versus the absence of a natural classification [ 8 ]. The classification in critical (ie, borderline) cases is difficult, particularly when a categorical system of diagnosis is considered.

Fuzzy logic plays an important role in medicine [ 7 , 9 – 14 ]. Some examples showing that fuzzy logic crosses many disease groups are the following.

• To predict the response to treatment with citalopram in alcohol dependence [ 15 ].
• To analyze diabetic neuropathy [ 16 ] and to detect early diabetic retinopathy [ 17 ].
• To determine appropriate lithium dosage [ 18 , 19 ].
• To calculate volumes of brain tissue from magnetic resonance imaging (MRI) [ 20 ], and to analyze functional MRI data [ 21 ].
• To characterize stroke subtypes and coexisting causes of ischemic stroke [ 1 , 3 , 22 , 23 ].
• To improve decision-making in radiation therapy [ 24 ].
• To control hypertension during anesthesia [ 25 ].
• To determine flexor-tendon repair techniques [ 26 ].
• To detect breast cancer [ 27 , 28 ], lung cancer [ 28 ], or prostate cancer [ 29 ].
• To assist the diagnosis of central nervous systems tumors (astrocytic tumors) [ 30 ].
• To discriminate benign skin lesions from malignant melanomas [ 31 ].
• To visualize nerve fibers in the human brain [ 32 ].
• To represent quantitative estimates of drug use [ 33 ].
• To study the auditory P50 component in schizophrenia [ 34 ].
• to study fuzzy epidemics [ 35 ],
• to make decisions in nursing [ 36 ],
• to overcome electroacupuncture accommodation [ 37 ].

We used the database MEDLINE to identify the medical publications using fuzzy logic. We used as keywords fuzzy logic and grade of membership . The total number of articles per year appears in Table 1 . The data is from 1991 to 2002 and includes also the number of those publications in 1990 and before. It results in a total of 804 articles and agrees essentially with the numbers indicated in [ 7 , 13 ]. We plan to screen databases in the engineering literature that covers medicine-related articles since it is difficult to publish medical results using a fuzzy logic approach. In the future we will compare the figures obtained.

Number of papers per year in medicine using fuzzy logic.

Figure 1 indicates an exponential growth in the number of articles in medicine making use of fuzzy technology. The preliminary data we have for 2003 and 2004 [ 38 ] supports this tendency.

Number of publications per year indexed in MEDLINE using fuzzy logic.

FUZZY LOGIC IN BIOINFORMATICS

Bioinformatics derives knowledge from computer analysis of biological data. This data can consist of the information stored in the genetic code, and also experimental results (and hence imprecision) from various sources, patient statistics, and scientific literature. Bioinformatics combines computer science, biology, physical and chemical principles, and tools for analysis and modeling of large sets of biological data, the managing of chronic diseases, the study of molecular computing, cloning, and the development of training tools of bio-computing systems [ 39 ]. Bioinformatics is a very active and attractive research field with a high impact in new technological development [ 40 ].

Molecular biologists are currently engaged in some of the most impressive data collection projects. Recent genome-sequencing projects are generating an enormous amount of data related to the function and the structure of biological molecules and sequences. Other complementary high-throughput technologies, such as DNA microarrays, are rapidly generating large amounts of data that are too overwhelming for conventional approaches to biological data analysis. We have at our disposal a large number of genomes, protein structures, genes with their corresponding expressions monitored in experiments, and single-nucleotide polymorphisms (SNPs) [ 41 ]. For example, the EMBL Nucleotide Sequence Database ( http://www.ebi.ac.uk/embl ) has increased in 12 months from 18.3 million entries comprising 23 Gb (Release 71, September 2002) to 27.2 million entries comprising over 33 Gb (Release 76, September 2003) as indicated in [ 42 ].

Handling this massive amount of data, in many cases imprecise and fuzzy, requires powerful integrated bioinformatics systems and new technologies.

Fuzzy logic and fuzzy technology are now frequently used in bioinformatics. The following are some examples.

• To increase the flexibility of protein motifs [ 43 ].
• To study differences between polynucleotides [ 44 ].
• To analyze experimental expression data [ 45 ] using fuzzy adaptive resonance theory.
• To align sequences based on a fuzzy recast of a dynamic programming algorithm [ 46 ].
• DNA sequencing using genetic fuzzy systems [ 47 ].
• To cluster genes from microarray data [ 48 ].
• To predict proteins subcellular locations from their dipeptide composition [ 49 ] using fuzzy k-nearest neighbors algorithm.
• To simulate complex traits influenced by genes with fuzzy-valued effects in pedigreed populations [ 50 ].
• To attribute cluster membership values to genes [ 51 ] applying a fuzzy partitioning method, fuzzy C-means.
• To map specific sequence patterns to putative functional classes since evolutionary comparison leads to efficient functional characterization of hypothetical proteins [ 52 ]. The authors used a fuzzy alignment model.
• To analyze gene expression data [ 53 ].
• To unravel functional and ancestral relationships between proteins via fuzzy alignment methods [ 54 ], or using a generalized radial basis function neural network architecture that generates fuzzy classification rules [ 55 ].
• To analyze the relationships between genes and decipher a genetic network [ 56 ].
• To process complementary deoxyribonucleic acid (cDNA) microarray images [ 57 ]. The procedure should be automated due to the large number of spots and it is achieved using a fuzzy vector filtering framework.
• To classify amino acid sequences into different superfamilies [ 58 ].

THE FUZZY HYPERCUBE

In 1992, Kosko [ 4 ] introduced a geometrical interpretation of fuzzy sets as points in a hypercube. In 1998, Helgason and Jobe [ 1 ] used the unit hypercube to represent concomitant mechanisms in stroke. Indeed, for a given set

a fuzzy subset is just a mapping

and the value μ( x ) expresses the grade of membership of the element x ∈ X to the fuzzy subset μ.

For example, let X be the set of persons of some population and let the fuzzy set μ be defined as healthy subjects . If John is a member of the population (the set X ), then, μ (John) gives the grade of healthiness of John, or the grade of membership of John to the set of healthy subjects . If λ is the fuzzy set that describes the grade of depression, then λ (Mary) is the degree of depression of Mary.

Thus, the set of all fuzzy subsets (of X ) is precisely the unit hypercube I n = [0, 1] n , as any fuzzy subset μ determines a point P ∈ I n given by P = (μ( x 1 ), …, μ( x n )). Reciprocally, any point A = ( a 1 , …,  a n ) ∈  I n generates a fuzzy subset μ defined by μ( x i ) = a i , i = 1, …,  n . Nonfuzzy or crisp subsets of x are given by mappings x : X  → {0, 1}, and are located at the 2 n corners of the n -dimensional unit hypercube I n . For graphic representations of the two-dimensional and three-dimensional hypercube, we refer to [ 59 ].

, not both equal to the empty set not both equal to the empty ∅=(0,0,…,0), we define the difference between p and q as

Of course d ( ∅, ∅) = 0. We know that d is indeed a metric [ 60 ]. Hypercubical calculus has been described in [ 61 ], while some biomedical applications of the fuzzy unit hypercube are given in [ 1 , 6 , 59 ]. Recently, the fuzzy hypercube has been utilized to study differences between polynucleotides [ 59 ] and to compare genomes [ 44 , 62 ].

AN APPLICATION TO DRUG ADDICTIONS

We now present an example of the use of the fuzzy hypercube in a medical case of consumption of drugs.

Consider the following fuzzy variables: smoking and alcohol drinking . If you do not smoke, then your degree of being a smoker is evidently 0. If you smoke, for example, six cigarettes per day, we say that your degree of being a smoker is 0.8. If the consumption is ten or more, the degree is 1. See [ 63 Figure 3.8] for a geometrical representation of the fuzzy concept of being a smoker.

With respect to the other fuzzy variable, if you drink no alcohol, the degree of this variable is 0. If you drink more than 75 cc of alcohol per day, the degree of alcoholism is 1. For 25 cc/d, the degree could be 0.4 and for 50 cc/d, 0.8.

Thus, the fuzzy set μ = (0, 0) corresponds to a nonsmoker and teetotaler. Some further examples are the following: the set μ = (1, 0) represents a heavy smoker, but a teetotaler, and the set μ = (0.8, 1) is a person who smokes about six cigarettes a day and is a risk consumer of alcohol.

Suppose you correspond to the fuzzy set λ = (1, 1), have recently had some health problems, and your physician has advised you to reduce your consumption of cigarettes and alcohol by half. The ideal situation for your health is, of course, the point μ = (0, 0), but it is possibly difficult to achieve.

Cigarette smoking and alcohol drinking during adolescence have been shown to be associated with a greater possibility of concurrent and future substance-related disorders (Lewinsohn etal [ 64 ]; Nelson and Wittchen [ 65 ]). In order to report patterns of drug use and to describe factors associated with substance use in adolescents, a cross-sectional survey was carried out in a representative population sample of 2550 adolescents, aged 12 to 17 years, from Galicia (an autonomous region located in the Northwest of Spain). The original survey covered the use of alcohol, tobacco, illicit drugs, and other psychoactive substances. For tobacco smoking and alcohol drinking, each subject of the population sample was assigned a fuzzy degree of addiction (or risk use) and mapped into the two-dimensional hypercube I 2 by an expert.

Several subjects occupy the same point in the two-dimensional hypercube. For example Figure 2 represents the number of subjects in the cross-sectional survey according to the two fuzzy degrees of addiction. The reader can see that there are 1278 subjects corresponding to the point (0,0), that is, nonsmoker and teetotaler. Also 7 adolescents are at the point (0.8,0.2). There are 121 subjects on the line of probability x 1 + x 2 = 1. Indeed (see Figure 2 ), 23 + 1 + 1 + 2 + 2 + 7 + 1 + 84 = 121.

Number of subjects in the two-dimensional fuzzy hypercube I 2 .

Most subjects were inside the hypercube but outside the line of probability. This means that the vast majority of subjects (2429/2550 ≈ 95.25 % ) are outside the line of probability. This is in agreement with the fundamental limitation of probability theory with respect to clinical science in general [ 1 ] and agrees with its results (29/30 ≈ 96.66 % ).

We refer to [ 59 ] for details on the general theory of fuzzy midpoints and their applications. It has been used recently to average biopolymers [ 66 ].

AN APPLICATION TO THE COMPARISON OF GENOMES

Whole genome sequence comparison is important in bioinformatics [ 44 , 67 ].

The complete genome sequence of Mycobacterium tuberculosis H37Rv is available at http://www.ncbi.nlm.nih.gov with accession number NC – 000962.

The genome comprises 4 411 529 base pairs, contains around 4000 genes, and has a very high guanine+cytosine content [ 68 ]. Computing [ 44 ] the number of the nucleotides at the three base sites of a codon in the coding sequences of M tuberculosis ( Table 2 ), and then calculating the corresponding fractions, we have the fuzzy set of frequencies of the genome sequence of M tuberculosis ( Table 3 ). This set can be considered as a point in the hypercube I 12 . Indeed, the point

Number of nucleotides at the three base sites of a codon in the coding sequence of Mycobacterium tuberculosis .

Fractions of nucleotides at the three base sites of a codon in the coding sequence of Mycobacterium tuberculosis .

Aquifex aeolicus was one of the earliest diverging, and is one of the most thermophilic, bacteria known [ 69 ]. It can grow on hydrogen, oxygen, carbon dioxide, and mineral salts. The complex metabolic machinery needed for A aeolicus to function as a chemolithoautotroph (an organism which uses an inorganic carbon source for biosynthesis and an inorganic chemical energy source) is encoded within a genome that is only one-third the size of the E coli genome.

The corresponding data for A aeolicus was obtained from http://www.ncbi.nlm.nih.gov with accession number {"type":"entrez-nucleotide","attrs":{"text":"NC_000918","term_id":"15282445","term_text":"NC_000918"}} NC_000918 , and is presented in Tables ​ Tables4 4 and ​ and5, 5 , respectively. The complete genome sequence has 1 551 335 base pairs. The fuzzy set of frequencies of the genome of A aeolicus is

Number of nucleotides at the three base sites of a codon in the coding sequence of Aquifex aeolicus .

Fractions of nucleotides at the three base sites of a codon in the coding sequence of Aquifex aeolicus .

Using the distance given in (5) , it is possible to compute the distance between these two fuzzy sets representing the frequencies of the nucleotides of A aeolicus and M tuberculosis :

In [ 44 ] we calculate the difference between M tuberculosis and E coli K-12 obtaining

Using the corresponding data for E coli (see [ 44 Tables ​ Tables3 3 and ​ and3]), 3 ]), we get

ACKNOWLEDGMENTS

This research is partially supported by Ministerio de Educación y Ciencia and FEDER, Projects MTM2004–06652–C03–01 and MTM2004–06652–C03–01, and by Xunta de Galicia and FEDER, Project PGIDIT05PXIC20702PN.

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Fuzzy Logic and Hybrid based Approaches for the Risk of Heart Disease Detection: State-of-the-Art Review

• Review Paper
• Published: 02 August 2021
• Volume 103 , pages 681–697, ( 2022 )

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• Jagmohan Kaur   ORCID: orcid.org/0000-0001-8426-596X 1 &
• Baljit S. Khehra 2  

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Artificial Intelligence, Machine Learning, Fuzzy Logic, Neural Network, Genetic Algorithm and their hybrid systems play vital role in the medical sciences to diagnose various diseases efficiently in the patients. The problems related to the heart are widely comon in today’s world. The risk of heart failure develops due to the narrowness and blockage in the coronary arteries of the heart as excess cholesterol deposits in the arteries and blood vessels that results in fatigue, chest pain, dyspnoea, sleeping difficulties and depression. This research aims to explore diverse work done on FL and Hybrid-based techniques to identify the risk of heart disease among the patients. The present study reveals publications along with the strength, operating system, accuracy rate and other specifications used in the identification of heart disease based on FL and Hybrid-based approaches since 2010. This survey contributes motivation for research scholars to generate more innovative ideas and continue their research work in the respective field. Moreover, the future model for direct service of the patients from old age homes to the Intensive Care Unit through ambulance services is also presented in this paper.

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G. Thippa Reddy, M. Praveen Kumar Reddy, … Gautam Srivastava

Avoid common mistakes on your manuscript.

Introduction

The heart disease involves many risks like gender, age, obesity, high blood pressure, high cholesterol, diabetes, family history, drinking alcohol and smoke. Apart from these, there are many other threats like underemployment industrialization, stress due to over work, physical inactivity, depression, stress, diet/routine changes and distressed sleep have increased in this technical and modern world. In addition to this, change in life style, egoism, greed and narcissistic approach of people have triggered the occurrence of chronic diseases in patients.

Heart diseases are categorized into distinct types like congenital heart disease, coronary heart disease (CHD), arrhythmia, dilated cardiomyopathy, heart failure, myocardial infarction (MI), hypertropic cardiomyopathy and mitral regurgitation. The patient having heart problem may feel chest pain, faintness or coolness in arms and legs. However, controlling blood pressure, eating a well-balanced nutritious diet, regulating exercise regime, limited usage of alcohol, tobacco, smoking and gazettes can treat illness and malfunction of the heart.

The mortality rate of the heart patients is the highest in two countries namely: Africa and India, which is 34% and 23%, respectively, and it is the lowest in France, Japan and Hong Kong. Both developed and underdeveloped countries have been facing this chronic disease since four decades due to the excess consumption of alcohol, smoking and tobacco. Nowadays, the most of the deaths occur due to coronary heart disease. However, in some European countries, death rate due to heart failure has declined as they are followed by better health/education services and other preventive measures. According to the report of WHO [ 1 ], near 17.8 million older and adults face this deadly disease. In fact, the death rate in adults is greater than that of the aged people. Centers for Disease Control and Prevention (CDC) [ 2 ] have announced that ratio of death rate in Americans is 1:4 that means one out of every four is dead due to heart stroke and 1 out of each 5 people doesn’t know that they are affected by silent attack. One more description from British Heart Foundation (BHF) [ 3 ] revealed that the panic of pandemic COVID-19 (coronavirus disease) in the year 2020 has become the reason of people dying with heart stroke due to psychological stress and social distancing. All this has even affected the economy of the world as well as of other countries.

With the advancement of power of computer applications can make drastic changes in the medical field by predicting disorder of tumors, lungs, thyroids and heart at very early stage in the patients. Computer-aided heart disease risk diagnose system has many features:

Modern technique

Time saving

Independent from medical experts

Minimize expenditure

Minimal errors

Less human effort

Diminish mortality rate

This era of artificial intelligence comes up with another invention made by the scholars of the Oxford University [ 4 ], well known as “fingerprint” a biomarker named as FRP (Fat Radiomic Profile) which is helpful in diagnosing future stroke via scarring and inflammation of blood vessels. The British Heart Foundation (BHF) and the National Institute of Health Research (NIHR) are providing funds for the same.

Research Methodology

The selection and collection of papers in journals and international conferences have been chosen from state-of-the-art and well-recognized publishers that ensures the quality of this review paper. Total 53 papers are summarized in this paper, out of which 4 revealed the status of heart disease patients in the world by WHO, BHF, NIHR and CDC and rest 49 papers bring forward current approaches and algorithms of AI being used for the identification of heart risk since 2010. In the Fig. 1 , pie chart shows 73% of area of publications is covered by hybrid system and 27% belongs to FL.

Publications of fuzzy logic and hybrid system

Further, references of 21 IEEE, 13 Springer, 9 Elsevier and 4 ACM papers are provided to bring forward the distinct techniques and their combinations being used in heart disease detection along with their data bases, approaches, accuracy and other specifications. Collection of research papers per year and per publication is presented in Figs. 2 and 3 , respectively. The Table 1 reveals total number of publications of SCI Index.

Collection of research papers per year

Collection of research papers per publisher

Table of Abbreviations of Symptoms and Heart Disease Database

The following Tables 2 and 3 give the information of abbreviations used for symptoms and heart disease database throughout the paper.

Review of FL and Hybrid-Based Approaches for the Risk of Heart Disease Detection

A mathematical discipline in which the structure of human behavior in the form of uncertainties, true or false forms the basis of FL. FL has following features:

Fascinating area of research

Computational approach

A matter of degrees of truth

A limiting case of estimated reasoning

Performs decision-making with approximate values

The flow chart of algorithm of Fuzzy logic-based approach for the risk of heart disease is shown in the Fig. 4 . The combination of two or more than two technologies to find the solution of the peculiar problem, overcome the deficiency of one technique and strengthen the system are known as hybrid systems. In this study, hybridization of techniques has been described as,  FL [ 8 , 9 , 11 , 12 , 14 , 15 , 19 , 20 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 35 , 36 , 38 , 39 , 40 , 41 , 45 , 48 , 50 , 52 , 53 ], GA [ 5 , 7 , 10 , 14 , 18 , 26 , 27 , 36 , 44 ], Artificial Neural Network (ANN) [ 5 , 7 , 10 , 13 , 35 , 42 , 43 , 44 , 51 ], Particle Swarm Optimization (PSO) [ 13 , 33 , 41 ], Ant Colony Optimization (ACO) [ 37 ], Naive Bayes (NB) [ 16 , 18 , 23 , 29 , 34 ], Decision Tree (DT) [ 8 , 18 , 20 , 22 , 23 , 28 , 41 , 48 , 51 ], K-means Clustering Algorithm [ 22 ], Logistic Regression (LR) [ 23 , 42 ], Multivariate Adaptive Regression Splines (MARS) [ 42 ], Rough Set (RS) [ 3 , 42 ], Support Vector Machine (SVM) [ 33 , 34 ], Random Forest (RF) [ 21 , 23 ], K-Nearest Neighbourhood (K-NN) [ 18 , 30 , 37 , 46 ], Logistic Regression SVM (LR SVM) algorithm in [ 23 ], has been summarized.

Flow chart of algorithm of FL-based approach for the risk of heart disease detection

Review of Research Papers from 2010–2013 of FL and Hybrid-Based Approaches

Adeli et al. [ 52 ] demonstrated the fuzzy expert system (2010) using 11 input attributes from database of CCF, LBF and V.A medical Center: AG, CP, CHL, MHR, RBS, RECG, THR, BP, OP, GR, EXANG and 1 output attribute with 5 features: sick (s1-s4) and healthy. Fuzzification was structured in trapezoidal, triangular, R and L membership functions. Implementation of Mamdani inference system was made with rule-based system of 44 rules. ‘COG’ technique was used for defuzzification and yielded 94% accuracy. Design of the system was implemented in MATLAB. Explanation of hybrid fuzzy-evidential inference engine (2010) was made by Vahib Khatibi et al. [ 39 ] using fuzzy sets and Demster–Shafer theory of evidence. The hybrid system achieved 91.58% accuracy from the data set of patients from V.A medical Center, CCF, HIC and UHS.

An article (2011) by Anooj in [ 40 ] revealed the system based on self-received information from the database. Extension in a clinical decision support system was made by using triangular membership functions along with Mamdani fuzzy inference system in programming language MATLAB 7.10. Defuzzification technique ‘COA’ was utilized to achieve 62.35% of accuracy rate. CCF, V.A medical center and UHS were the main sources of database. E. P. Ephzibah in the paper [ 26 ] presented a hybrid system (2011) based on GA and FL in MATLAB 7.3.0 for the smooth work in healthcare field. CCF data set was used for the implementation of the work. Due to GA, 14 selected attributes were reduced to 6 attributes: CP, RBP, EXANG, MHR, OP and CA. Trapezium and triangular membership functions were used in the strategy of fuzzification. Another development in the framework of fuzzy expert system (2012) was initiated by Bhuvaneswari Amma [ 5 ] to demonstrate an adaptable disease diagnosis system using hybridization of GA along with NN. It consisted of 13 input variables AG, CP, GR, CHL, RBP, FBS, THS, RECG, MHR, EXANG, OP, CA, SLOPE and 1 output variable for the data base of UIC, Irvine. Accuracy rate was obtained 94.17% which was evaluated through Root Mean Square Error. The system (2012) described by Ephzibah et al. [ 27 ] made use of GA to select salient and 6 prime features responsible for the rapid and error free diagnosis of disease and then implemented FL. MATLAB was used as programming language for the data base taken from UCI ML respository. Akhil jabbar et al. [ 6 ] revealed the methodology (2012) of association rules which were generated by using hybrid feature subset selection. The paper consisted of mainly 11 input variables: AG, GR, THALACH, LDL CHL, HDL CHL, CHOL, Rural/Urban, BP Systolic, BP Diastolic and Serum Triglycerides. Approach was implemented in the database of Andra Pradesh which yielded 95% accuracy.

The another system (2012) designed by Muthukaruppan [ 41 ] was based on DT and PSO containing 13 input variables: AG, CHOL, BP, GR, THALACH, CP, RECG, OP, EXANG, SLOPE, THAL, CA and 1 output variable. The phenomenon of ‘if-then’ rule in fuzzy rule-base was applied. The system was designed in MATLAB 7 and yielded accuracy of 93.27%.

The demonstration of another fuzzy expert system (2013) was presented by Sanjeev Kumar et al. [ 53 ]. It explained 6 input variables: CP, BS, BP, CHL, MHR, OP and one is decision variable with 5 features. Mamdani inference system was implemented with rule-based system (22 rules). Rule base was characterized by ‘if-then’ rules using logical combinations of inputs with AND operator in MATLAB. Center of Gravity (COG) approach was applied for defuzzification, and database was taken from Smt. Parvati Devi hospital, EMC hospital, medical center, Amritsar with accuracy of 92%. The demonstration of another fuzzy expert system (2013) was presented by Syed Umar Amin et al. [ 7 ] using a hybrid system of ANN along with GA for prediction of heart disease. Total 12 input variables: GR, AG, CHL, BP, FAMHIST, SMOKE, alcohol intake, physical activity, DM, diet, OBES, stress and 1 output variable were used. The article used input (12), hidden (10) and output (2) nodes, respectively. Implementation was done in MATLAB R2012a. Accuracy of 92% was measured by applying least mean square error (MSE). Jae-Kwon Kim et al. [ 28 ] represented prediction model (2013) of heart disease in MATLAB to overcome the uncertainty received from the medical experts by using FL and GA with an accuracy of 69.22%. The fuzzy rule base generated ‘if-then’ rules by making use of C4.5 algorithm of the DT. Experiment was conducted on 299 patients of Gill medical center, Korea by taking 7 input variables GR, AG, CHL, HDL CHL, RBP, DM and SMOKE. The Table 4 presents the list of research papers from 2010–2013 of FL and Hybrid-based approaches.

Review of Research Papers from 2014–2017 of FL and Hybrid-Based Approaches

Explanation of hybrid model (2014) was made by Yuehjen E. Shao et al. [ 42 ] consisted of many hybrid approaches MARS, LR, RS and ANN techniques. Input variables: AG, CP, GR, RBP, FBS, Serum CHOL, RECG, EXANG, THALACH, OP, CA, THAL were used in this hybrid model and attained 83.93% accuracy evaluated by Root Mean Square Error in RESE software. Jan Bohacik et al. [ 8 ] applied cumulative application of FL Controller and DT in heart disease diagnosis (2014). Coding was developed in weka tool with a data base from Hull York medical school and University of Hull, England with sensitivity and specificity 34.23% and 91.01% respectively.

Again Jan Bohacik et al. [ 9 ] developed an Algorithmic Model (2015) for heart disease patients by employing the same on 2032 patients of Hull York medical school and University of Hull, England with an accurate rate 64.41% and specificity 63.27%. The system considered 9 input variables: BCL, BUAL, GR, BSL, AG, WT, PR, HT and NT-proBNPlevel. Software tool Java was implemented in fuzzy inference system. The hybrid technique (2015) designed by Ankita Dewan [ 10 ] evolved a prototype to find and execute unknown information from the database of heart disease. Genetic Algorithm was hybrid with back propagation method. The study used 20, 10 and 10 as input, hidden and output nodes, respectively. MATLAB R2012a was used for the implementation of the task. The proposed methodology achieved nearly 100% with least error but being stiffen in local minima, the system was unable to achieve the desired outcome. The focus of Hui Yang et al. [ 29 ] was to construct a hybrid model (2015) for the heart failure identification by combining FL and NB in MALLET operating system. The system made use of 7 main risk factors responsible for heart stroke extracted from UMLS database and yielded 91.5% accuracy with precision 88.4%. Krishnaiah et al. [ 30 ] developed a robust system (2015) using data mining techniques: FL Controller and K-NN algorithm with a capability of reducing uncertainty available in the medical data. Weka 3.6.6 was used in the system which got 91% accuracy. Mainly 13 input attributes : AG, CR, CP, RBP, CHOL, RECG, FBS, THALACH, EXANG, OP, SLOPE,CA, THAL were considered and testing was conducted on 550 patients of heart disease databases of CCF and Statlog.

The design of fuzzy expert engine (2016) was developed by Wiga Maulana et al. [ 11 ]. The system made use of 13 input variable: AG, CP, CHL, MNR, RBS, RECG, THAL, BP, OP, GR, EXANG, SLOPE, CA and 1 output variable: the status of angiography. The system used C4.5, CART and RIPPER in MATLAB (7.12 R2011a). The membership functions were optimized by imperialist competitive algorithm (ICA). The designed method was experimented on data sets from CCF and HIC, Budapest with an accuracy of 81.82%. Assemgul Duisenbayeva et al. [ 12 ] revealed more adaptable and compatible fuzzy inference system (2016) that assist doctors and physicians in their decision-making for CAD disease. CP, BP, LDL CHL, BS, GR, MHR and AG were 7 input and 1 output variable having 5 features: sick (s1–s4), healthy. The given approach was implemented in MATLAB. Coronary heart disease prediction system (2016) was developed by Mokeddem et al. [ 48 ] hybrid with SIPINA Decision Tree algorithm and Fuzzy logic. The system used 13 input features from the well-known CCF, HIC, LBF and UCI heart disease data sets using triangular, trapezoidal, R and L membership functions. ‘if-then’ rules were used in rule-base using logical combinations of inputs with AND operator. Centroid method was used for defuzzification. This new approach has yielded an accuracy of 94.05%. Feshki et al. [ 13 ] proposed the system of diagnosis (2016) that yielded results in less time and cost with an accuracy of 91.94%. AG, CP, RBP upon admission in hospital, GR, CHL, FBS, CA, RECG results, EXANG, MHR, OP, SLOPE and thalassemia were 13 attributes considered in this paper. The Particle Swarm Optimization was implemented to extract 8 features. Further, Feed Forward Back-Propagation Neural network (FFBPNN) was applied to optimize the PSO algorithm. Cleveland Clinic Foundation (CCF) data set was used. Fuzzy Decision Support System (2016) to predict heart disease was applied by Animesh Kumar Paul et al. [ 14 ] to pre-process data set, select effective attributes and then to make a strategy of fuzzy rule base. Accuracy of this approach is very close to near 80%. CCF, HIC, UHS and V. A. medical center heart disease datasets from the UCI ML repository were used in this system. C++ was used to implement the system.

An overview of fuzzy logic controller (2017) for coronary heart disease with 9 input variables: AG, CHL, BS, CP, ECG, HR,EX, GR, SMOKE and 1 output variable with 5 features was proposed by Mohammad Alqudah [ 31 ]. Trapezoidal, triangular, R, and L membership functions were used for all variables. Mamdani inference system with rule-based system (66 rules) using logical combinations of inputs with ‘AND’ operator was implemented on patients’ records in Jordan’. Coding was done in Visual Studio 2010 C which accomplished the diagnosis by yielding high accuracy. Tanmey Kasbe et al. [ 15 ] designed fuzzy expert system (2017) with 10 input variables: CP, CHOL, SBP, FBS, MHR, ECG, THAL, OP, AG, GR and 1 output variable with 5 parameters. Mamdani inference mechanism was implemented with rule-based system (86 rules) characterized by ‘if-then’ rules using logical combinations of attributes with AND/OR operator. Fuzzification was accomplished using triangular and trapezoidal membership function. MATLAB R2008 tool was used as programming language and Center of Gravity (COG) approach was applied for defuzzification and finally achieved 93.33% accuracy. V.A medical center, CCF and LBF were data set sources. Coronary illness framework (2017) was applied by Purushottam Sharma et al. [ 32 ] considered 13 input attributes: AG, GR, CP, FBS, RBP, RECG, THALACH, EXANG, OP, SLOPE, CA, THAL and CHOL from the data set of Hungary, Switzerland and U.S. The paper made use of very common combination of FL and GA, and brought 88.11% accuracy. Creation of accurate rule set was the main theme of this article. With a purpose of improvement in accuracy and reduction in computational time Kanika Pahwa and Ravinder Kumar [ 16 ] proposed prediction method of heart disease (2017) by hybridization of techniques NB and RF. Both these techniques yielded 84.15% and 84.16% accuracy, respectively. Kaan Uyar et al. [ 43 ] presented diagnosis of heart disease model (2017) using 13 input attributes: AG, GR, CP, RBP, CHOL, FBS, RECG, THALACH, EXANG, OP, SLOPE, CA and THAL. GA-based Recurrent Fuzzy Neural Network (RFNN) involved 13 input, 7 hidden and 1 output neurons. An accuracy of 97.78% was yielded by experimentation on CCF patients’ data set which was further evaluated by RMSE (Root Mean Square Error). Programming Languages Ubuntu and Java were used for the implementation of the system. Utilization of hybrid data mining techniques (2017) was demonstrated by Meenal Saini et al. [ 17 ] using 13 attributes AG, GR, CP, RBP, CHOL, FBS, RECG, CA, THAL, EXANG, THALACH, OP and SLOPE. This approach has considered hybridization of 9 classifiers classifiers: SVM, Decision tree, Neural Network, Bayesian regularized NN, Generalized linear model, Lasso, MARS, Classification and Regression Tree and come out with an accuracy of 82.54%. Arabasadi et al. [ 44 ] presented an adaptive and affordable technique (2017) for the enhancement of accuracy and finally achieved 93.85%. The system combined together GA and NN, and involved 22 input, 5 hidden and 1 output neurons. Experimentations were done on 303 patients with data set from HIC, CCF and LBF. The identification of heart disease diagnosis (2017) was derived by Abhishek Rairikar et al. [ 18 ] using hybridization of GA, DT and KNN. The use of 13 vital clinical attributes was considered to achieve considerable accuracy rate. The Table 5 presents the list of research papers from 2014–2017 of FL and Hybrid-based approaches.

Review of Research Papers from 2018–2020 of FL and Hybridbased Approaches

Explanation of a mediative fuzzy logic system (2018) given by Ion Iancu [ 45 ] has considered 11 input variables: CP, CHL, BP, MHR, BS, RECG, EX, THAL, OP, AG, GR and 1 output variable with 5 features. Mamdani inference system was implemented with rule-based system (44 rules) using ‘single input-single output’ phenomenon. Software MATLAB was used for the implementation of experimental work from the data base of CCF, V. H. medical center and LBF. Defuzzification was done using ‘Middle of maxima and middle of minima’ approach. Hasan Kahtan et al. [ 49 ] proposed a FL system with 4 inputs variables: AG, BS, BP and CHL. Fuzzification was done using trapezoidal membership function for all variables. A rule-based system (96) was implemented in JAVA (using Net Beans IDE 8.2 in Java) with an accuracy of 98%. The Fuzzy Inference System (2018) designed by Vishu Madaan et al. [ 19 ] has resolved a peculiar problem of diagnosis by making use of 6 input parameters: AG, BP, CP, CHL, HR and DM. The rule base set contained 162 rules (if-then rule) with the implementation in MATLAB tool. The proposed model has acquired 82.65% accuracy. Another hybrid system (2018) based on FL controller and DT was described by Oumaima Terrada et al. [ 20 ] using 14 clinical input parameters: Total CHL, HDL, LDL, HBP, SMOKE, OBES, DM, GR, BMI, SBP, TRIG, AG, FAMHIS and sedentary lifestyle. Software MATLAB was used the experiments of diagnosis for the rule base consisting of logical combinations of AND operator and gave 63.24% accuracy.

The study developed by Prerna Jain et al. [ 50 ], displayed the system (2019) considering 8 input variables: AG, CHL, GR, OBY, HTN, DM, FAMHIS, SMOKE and 1 output variable with 3 parameters. Fuzzification was done using triangular and trapezoidal membership functions for each and every all input variable. Mamdani approach was used in rule base system (44 rules) using if-else statements. The system was designed in programming language MATLAB and achieved 91% of accuracy. J. Vijayashree et al. [ 33 ] presented ML framework (2019) using 11 input attributes: AG, GR, CP, RBP, FBS, CHOL, CA, OP, RECG, SLOPE and THALACH. Hybridization of PSO-SVM was utilized and compared with other classifiers and using the data base of staLog heart disease set and yielded 88.22% accuracy results and implementation was done in MATLAB. The Hybrid system (2019) was expanded by M. Tarawnah et al. [ 34 ] for heart disease identification. The system comprised of 11 input variables from the data base of CCF and UCI ML respository. Implementation of classification techniques NB, SVM, J4.8, NN, GA and RF was shown and compared with the hybrid approach of all techniques. Accuracy obtained was 89.2% and it was achieved by hybrid approach which was better than all other approaches. Senthil kumar Mohan et al. [ 21 ] used hybrid ML techniques (RF and Linear Model (HRFLM)) to demonstrate an effective heart disease prediction framework (2019) with an accuracy of 88.7%. The study made use of 13 attributes: AG, GR, CP, RBP, CHOL, FBS, RECG, OP, SLOPE, CA, THAL, MHR and EXANG. Classification of heart disease was done in R Studio Rattle software tool using the data of 297 patients obtained from CCF data set. Heart disease detection hybrid classifier (2019) was represented by Yukti Sharma [ 22 ] using hybridization of DT and K-Means Clustering. The study considered 14 attributes namely: AG, GR, CP, BP, CHL level, BS, ECG, THAL, CA and SLOPE obtained from CCF data base. Classifier K-Means Clustering and Decision Tree obtained 49% and 52% accuracy, respectively, and the proposed work of hybrid classifier yielded 62% accuracy which was greater than that of individual classifiers. Saba Bashir et al. [ 23 ] gave an emphasis on approaches and algorithms of attribute selection in datasets of heart disease diagnosis system (2019) using 4 classifiers. Logistic Regression SVM yielded 84.85% accuracy which is the highest among the accuracies obtained using DT (82.22%), LR (82.56%), RF (84.17%) and NB (84.24%) algorithms on UCI database in Rapid Miner Studio software tool. Presentation of a fuzzy-based framework (2019) was proposed by Padmavathi Kora et al. [ 46 ] for valvular heart disease detection by considering 7 clinical input variables: AG, BP, CHL, DM, BMI, SMOKE and physical activity with 1 output variable having 3 features. After training the dataset using NN, Mamdani inference framework was implemented with rule set system (44 rules) ‘if-then’ rules using logical combinations of inputs with AND operator. The source of dataset was CCF and HIC. Parameter ROC Curve (Receiver Operator Characterstic) was used to check the accuracy of 99.3% in MATLAB R2019b. The another proposal (2019) using Imperialist Competitive Algorithm (ICA) to select optimal features and K-nearest neighbor approach (KNN) was used to classify heart disease by J. Nourmohammad-Khiarak et al. [ 35 ]. The system was user-friendly in the strategy of feature selection as well as training and testing of data set and yielded accuracy of 88.25%. Testing was conducted on 303 patients with 13 clinical parameters of heart disease databases from UCI ML respository and T. S. Rajaei hospital. An intelligent medical heart diagnose system (2019) was designed by L. Ali et al. [ 24 ]. Data set was extracted from CCF which considered 13 input attributes out of 76 attributes: AG, CHOL, CA, CP, FBS, EXANG, RECG, THAL, THALACH, RBS, OP. After extracting noisy and redundant features using Chi-square statistical model, the proposed method used Deep Neural Network (DNN) to avoid underfitting and overfitting of network and achieved 93.33% accuracy.

A hybrid approach (2020) to predict heart disease was proposed by G. Thippa Reddy et al. [ 36 ] considering together adaptive GA with FL. The first step followed the selection of features through rough set theory and the implementation of hybrid AGAFL classifier is made in second step. The membership functions were designed in trapezoidal functions. The system consisted of 13 input variables, namely AG, RBP, GR, CHL, MHR, OP, CA, RECG, FBS, CP, SLOPE, THAL and EXANG. Experimental work was done with data base from CCF, HIC and UCI ML respository which obtained 90%, 91% and 89% accuracy, respectively. Preethi Krishnan et al. [ 25 ] proposed a novel clinical based and intuitive model (2020) for heart disease detection using fuzzy expert system whose accuracy, specificity and sensitivity were 96.6%, 96.8% and 95.6%, respectively, using MIT-BIH heart disease data base in Physionet. Better outcomes were generated to detect PVC beats in electrocardiogram signals [57-63]. Fuzzification was done using Gaussian and triangular membership functions. Explanation of another classical model (2020) was described by Anna Karen et al. [ 47 ] using 6 ML classifiers out of which maximum accuracy was achieved by (CHI-PCA) with RF where the data were derived from CH datasets [54-56] . The paper also revealed clear comparative study other classifiers using CCF, HIC and CH datasets in Apahe Spark 2.2.0. The prediction model (2020) of hybrid approach using ACO and Hybrid K-NN (HKNN) was designed by Sowmiya et al. [ 37 ]. Utilization of feature selection was made by ACO, and then another hybrid classifier was implemented in Netbeans IDE. Experiments were conducted in Netbeans IDE with an accuracy of 99.2% using data obtained from CCF. Comparison with other classifiers along with their accuracies was presented in this study. Mohammad Ali Hassani et al. [ 51 ] used hybrid ML techniques (NN and DT) to demonstrate a prouctive heart disease detection model (2020) with an accuracy of 98.7%. The study made use of 13 input attributes: AG, GR, CP, RBP, CHOL, FBS, RECG, OP, SLOPE, CA, THAL, THALACH and EXANG. Classification of heart disease was done in Weka software tool using the data of 227 patients obtained from CCF and StaLog heart disease data set. A new and unique hybrid technique (2021) using Fuzzy Logic along with Improved C4.5 algorithm was designed and implemented by Muhammad et al. [ 38 ]. The system consisted of 11 input variables, namely AG, RBP, glucose, LDL CHOL, HDL CHOL, triglycerides, BCL, BMI, MHR, CP and CHL. Mamdani approach was applied in the fuzzy inference engine of 87 rules, and defuzzification was completed by centroid method. The proposed technique was designed and implemented in the MATLAB tool. Experimental work was done with data base from State Ministry of health, Kano, Nigeria which obtained 94.55% accuracy. Testing dataset was of 100 patients implemented in MATLAB software. The Table 6 presents the list of research papers from 2018–2021 of FL and Hybrid-based approaches.

Comparative Analysis of Accuracies/Techniques

Accuracy of all respective years for FL and Hybrid System is considered and shown in Table 7 along with evaluation parameters. In the Figs. 5 and 6 , higher accuracy in that respective year is shown and further, comparative analysis of both system’s accuracies is presented in Fig. 7 along with technique used in that particular paper. All the papers come up with distinct techniques to improve the accuracy in the diagnosis system of heart. The highest accuracy (99.4%) is achieved by using Fuzzy Logic hybrid with Improved C4.5 algorithm in the current year 2021 [ 38 ]. Existence of uncertainty is always there in the detection of any disease. An extensive amount of research has been carried out by various researchers using FL on heart disease detection as FL has enough capability to diagnose heart disease. Therefore, to handle FL is more suitable but the only challenge in FL system is the optimization of rules. If rules are more, complexity of the system increases and if rules are less, system accuracy decreases. Hence, selection of optimal rules is a major problem in FL. After that the next and the most used techniques are ANN, GA and DT. ANN is indeed a robust and powerful algorithm still it faces the challenge of the implementation of the automatic detection of the disease due to the complex and complicated structure of the network. Though GA and DT are easy and simple to understand, yet GA is time-consuming algorithm and DT leads to overfitting of the data.

Year-wise accuracy rate using FL

Year-wise accuracy rate using hybrid system

Year-wise accuracy rate using FL and hybrid system

The paper presents concise information about the diverse work done by various scholars in the field of developing a heart disease detection algorithm and software using soft computing techniques. The paper is the result of in-depth study and analysis of various papers published year-on-year in various renowned journals on this subject. Key finding is that maximum publications are based on FL and FL Hybrid Systems to improve the accuracy using genetic fuzzy logic, fuzzy neural, Adaptive Neuro-Fuzzy, Genetic Neuro-Fuzzy and PSO with FL as FL has enough capability to diagnose the heart disease. Comparison of accuracy of various approaches has been presented graphically, and the best approach is also recommended. The paper also motivates young researchers and scholars to identify the gaps in existing work and take-up the work to create new models and optimize existing models. The efforts should be made to make cost-effective real-life software and tools which can be used by health institutions on a day-to-day basis helping to improve heart disease diagnostics.

Future Model of Fuzzy Logic

In future, model for direct service of the patients from the old age homes or other home care centers to the Intensive Care Unit (ICU) through ambulance services can be planned. An artificially intelligent system will take the data of clinical parameters from old age homes or other care centers. Fuzzy Logic system will be implemented to get the single output that will reveal distinct stages of patients in terms of healthy, first/second stage of sickness and critical stage. The system will show green color if the status of the person is healthy, and the respective person will be informed via SMS that you are ‘Healthy’. Otherwise, if the person is at the first/second stage of sickness, then a SMS ‘Do frequent monitoring’ will be sent to his/her mobile number. Furthermore, if the patient is at chronic stage of any disease, the system will show red color and the patient will be directly brought to the hospital. The Fig. 8 represents the future framework of the fuzzy logic system in any type of disease.

Future framework of fuzzy logic

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Kaur, J., Khehra, B.S. Fuzzy Logic and Hybrid based Approaches for the Risk of Heart Disease Detection: State-of-the-Art Review. J. Inst. Eng. India Ser. B 103 , 681–697 (2022). https://doi.org/10.1007/s40031-021-00644-z

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Received : 10 December 2020

Accepted : 30 May 2021

Published : 02 August 2021

Issue Date : April 2022

DOI : https://doi.org/10.1007/s40031-021-00644-z

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