Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set

P. Senthil Kumar ()

International Journal of System Assurance Engineering and Management, 2020, vol. 11, issue 1, No 14, 189-222

Abstract: Abstract In this article, the crisp, fuzzy and intuitionistic fuzzy optimization problem is formulated. The basic definitions and notations related to optimization problems are given in the preliminaries section. Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set is presented in this article. Then, with the help of the proposed algorithm the optimal solution of the crisp, fuzzy and intuitionistic fuzzy optimization problems are determined. A new theorem related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems is proposed and proved. Some new and concrete results related to type-2 fuzzy/type-2 intuitionistic fuzzy optimization problems are presented. To illustrate the proposed method, some real-life numerical examples are presented. The proposed article provides seven fully worked examples with screenshots of output summaries from the software used in the computations for better understanding. The advantages of the proposed approach as compared to other existing work are also specified. Detail analyses of the comparative study as well the discussion are given. To show the advantages of the proposed approach, superiority analysis is discussed. Comparison analysis and the advantages of the proposed operators are also discussed. Some managerial applications and the advantages of the proposed approach are given. Finally, conclusion and future research directions are also given.

Keywords: Fuzzy set; Fuzzy number; TFN; TrFN; Intuitionistic fuzzy set; Intuitionistic fuzzy number; TIFN; TrIFN; Type-2 FTP; Type-2 IFTP; Type-2 IFSTP; FAP; IFAP; IFSAP; Linear programming method; Integer programming problem; Optimal solution; Optimal assignment; PSK theorem (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (13)

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DOI: 10.1007/s13198-019-00941-3

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