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Intuitionistic fuzzy solid assignment problems: a software-based approach

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• Published: 23 May 2019
• Volume 10 , pages 661–675, ( 2019 )

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• P. Senthil Kumar   ORCID: orcid.org/0000-0003-4317-1021 1  

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This paper sustains a sound mathematical and computing background. In this paper, the software-based approach for solving intuitionistic fuzzy solid assignment problem (IFSAP) is presented. The IFSAP is formulated and it is solved by using Lingo 17.0 software tool. Theorems related to IFSAP is proved. The IFSAP and its crisp solid assignment problem both are solved at a time and their optimal solution is obtained. In addition, the optimal objective values of both the IFSAP and its crisp solid assignment problem (SAP) are estimated with the help of substituting the optimal solution(s) to their respective decision variables in the objective functions. Some new and important results are proposed. To illustrate the efficiency of the proposed method the numerical example is presented. The reliability of the proposed results are verified by using the numerical example. Strengths and weakness of the paper is mentioned. The novelty of the analysis is given into a coherent, concise, and meaningful manner of analysis. Social issue (real-life problem) is converted into a mathematical model and it is solved by the proposed method. At the end, the advantages of the proposed algorithm is explained.

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Acknowledgements

The author is grateful to anonymous referees for their constructive as well as helpful suggestions and comments to revise the paper in the present form.

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Kumar, P.S. Intuitionistic fuzzy solid assignment problems: a software-based approach. Int J Syst Assur Eng Manag 10 , 661–675 (2019). https://doi.org/10.1007/s13198-019-00794-w

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Received : 24 February 2018

Revised : 17 April 2019

Published : 23 May 2019

Issue Date : August 2019

DOI : https://doi.org/10.1007/s13198-019-00794-w

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Fuzzy Assignment problems

In this paper, we deal with solving a fuzzy Assignment Problem (FAP), in this problem C denotes the cost for assigning the n jobs to the n workers and C has been considered to be triangular fuzzy numbers. The Hungarian method is used for solving FAP by using ranking function for fuzzy costs. A numerical example is considered by incorporating a fuzzy numbers into the costs.

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I n the literature, there are various methods to solve assignment problems in which parameters are represented by triangular or trapezoidal fuzzy numbers. This paper presents an assignment problem with fuzzy costs, where the objective is to minimize the cost. Here each fuzzy cost is assumed as trapezoidal fuzzy number. A new ranking method has been used for ranking the fuzzy trapezoidal numbers. The fuzzy assignment problem has been transformed into a crisp one using ranking function and solved by branch and bound method. A numerical example is provided to demonstrate the proposed approach.

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www.ijera.com

Dr. P. Senthil Kumar (PSK), M.Sc., B.Ed., M.Phil., PGDCA., PGDAOR., Ph.D.,

In this paper, we investigate an assignment problem in which cost coefficients are triangular intuitionistic fuzzy numbers. In conventional assignment problem, cost is always certain. This paper develops an approach to solve an intuitionistic fuzzy assignment problem where cost is not deterministic numbers but imprecise ones. Here, the elements of the costs (profits) matrix of the assignment problem are triangular intuitionistic fuzzy numbers. Then its triangular shaped membership and non-membership functions are defined. A new ranking procedure which can be found in [4] and is used to compare the intuitionistic fuzzy numbers so that an Intuitionistic Fuzzy Hungarian method may be applied to solve the intuitionistic fuzzy assignment problem. Numerical examples show that an intuitionistic fuzzy ranking method offers an effective tool for handling an intuitionistic fuzzy assignment problem.

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