Spherical fuzzy sets and spherical fuzzy TOPSIS method

All the extensions of ordinary fuzzy sets with three dimensional membership functions such as intuitionistic fuzzy sets (IFS), intuitionistic fuzzy sets of second type (IFS2), and neutrosophic fuzzy sets (NFS) aim at defining the judgments of decision makers/ experts with a more detailed description...

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Bibliographic Details
Published inJournal of intelligent & fuzzy systems Vol. 36; no. 1; pp. 337 - 352
Main Authors Kutlu Gündoğdu, Fatma, Kahraman, Cengiz
Format Journal Article
LanguageEnglish
Published Amsterdam IOS Press BV 01.01.2019
Subjects
Decision making
Fuzzy sets
Judgments
Multiple criterion
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Summary:All the extensions of ordinary fuzzy sets with three dimensional membership functions such as intuitionistic fuzzy sets (IFS), intuitionistic fuzzy sets of second type (IFS2), and neutrosophic fuzzy sets (NFS) aim at defining the judgments of decision makers/ experts with a more detailed description. Introduction of generalized three dimensional spherical fuzzy sets (SFS) including some essential differences from the other fuzzy sets is presented in this paper. The new type of fuzzy sets is based on the spherical fuzzy distances which have been already defined in the literature. Arithmetic operations involving addition, subtraction and multiplication are presented together with their proofs. Aggregation operators, score and accuracy functions are developed. The multi-criteria decision making method TOPSIS is extended to spherical fuzzy TOPSIS and an illustrative example is presented. Additionally, a comparative analysis with intuitionistic fuzzy TOPSIS (IF-TOPSIS) is given.
ISSN:1064-1246
1875-8967
DOI:10.3233/JIFS-181401