The DOI matches its Crossref record; 31 of the 31 references it cites were found in a registry or an index.
Spherical fuzzy sets and spherical fuzzy TOPSIS method
Abstract
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.
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Cites
Zadeh, L. A. (1965) · Information and Control · doi:10.1016/s0019-9958(65)90241-x · Cited by 67,855
Atanassov, K. T. (1986) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(86)80034-3 · Cited by 16,465
The Concept of a Linguistic Variable and Its Application to Approximate Reasoning—I
Zadeh, L. A. (1975) · Information Sciences · doi:10.1016/0020-0255(75)90036-5 · Cited by 12,187
The concept of a linguistic variable and its application to approximate reasoning-III
Zadeh, L. A. (1975) · Information Sciences · doi:10.1016/0020-0255(75)90017-1 · Cited by 12,139
Atanassov, K. T. (1999) · Studies in Fuzziness and Soft Computing · doi:10.1007/978-3-7908-1870-3 · Cited by 2,017
Distances between intuitionistic fuzzy sets
Szmidt, E., & Kacprzyk, J. (2000) · Fuzzy Sets and Systems · doi:10.1016/s0165-0114(98)00244-9 · Cited by 1,627
Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets
Zhang, X., & Xu, Z. (2014) · International Journal of Intelligent Systems · doi:10.1002/int.21676 · Cited by 1,506
Boran, F. E., Genç, S., Kurt, M., & Akay, D. (2009) · Expert Systems with Applications · doi:10.1016/j.eswa.2009.03.039 · Cited by 1,500
Yager, R. R. (1986) · International Journal of General Systems · doi:10.1080/03081078608934952 · Cited by 725
Pythagorean fuzzy TODIM approach to multi-criteria decision making
Ren, P., Xu, Z., & Gou, X. (2016) · Applied Soft Computing · doi:10.1016/j.asoc.2015.12.020 · Cited by 599
Cited by
Simjanović, D. J., Zdravković, N., & Vesić, N. O. (2022) · Axioms · doi:10.3390/axioms11030105 · Cited by 25
Aleksić, A., Tadić, D., Komatina, N., & Nestić, S. (2025) · Mathematics · doi:10.3390/math13132216 · Cited by 11
Demircan, M. L. (2024) · Sakarya University Journal of Science · doi:10.16984/saufenbilder.1156767
Metadata
- Authors
- Kutlu Gündoğdu, F., & Kahraman, C.
- Venue
- Journal of Intelligent & Fuzzy Systems
- Publisher
- SAGE Publications
- Published
- 2018-11-28
- Volume
- 36
- Issue
- 1
- Pages
- 337-352
- ISSN
- 1064-1246 (ISSN-L)
- 1875-8967
- OpenAlex
- W2903466805
- Cited by
- 965
- References
- 31
- FWCI
- 47.17
- Type
- journal article
- Language
- en
- Open access
- closed
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