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Spherical fuzzy linear programming problem. (English) Zbl 1476.90359

Kahraman, Cengiz (ed.) et al., Decision making with spherical fuzzy sets. Theory and applications. Cham: Springer. Stud. Fuzziness Soft Comput. 392, 455-472 (2021).
Summary: The new extension of the uncertain set is presented by F. K. Gündoğdu and C. Kahraman [“Spherical fuzzy sets and spherical fuzzy TOPSIS method”, J. Intell. Fuzzy Syst. 36, No. 1, 337–352 (2019; doi:10.3233/jifs-181401)] and named as a spherical fuzzy set (SFS). The SFS is the superset of fuzzy, intuitionistic fuzzy, and Pythagorean fuzzy sets, respectively, [R. R. Yager, “Pythagorean fuzzy subsets”, in: Proceedings of the 2013 joint IFSA world congress and NAFIPS annual meeting, IFSA/NAFIPS 2013. Piscataway, NJ: IEEE Press. 57–61 (2013; doi:10.1109/ifsa-nafips.2013.6608375)]. The SFS inherently involves three membership functions, namely; positive, neutral, and negative membership degrees of the element into the SFS. In this chapter, we present the spherical fuzzy linear programming problem (SFLPP) in which the different parameters are represented by spherical fuzzy numbers (SFNs). The crisp version of the SFLPP is obtained with the aid of positive, neutral, and negative membership degrees. Furthermore, the spherical fuzzy optimization model is presented to solve the SFLPP. A numerical example and case study are presented to show the working efficiency of the proposed research. At last, the conclusion and future research scope are also discussed.
For the entire collection see [Zbl 1453.68015].

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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