Proportional Fuzzy Set Extensions and Imprecise Proportions

Kahraman, Cengiz

doi:10.15388/24-INFOR550

Informatica

Proportional Fuzzy Set Extensions and Imprecise Proportions

Volume 35, Issue 2 (2024), pp. 311–339

Cengiz Kahraman

https://doi.org/10.15388/24-INFOR550

Pub. online: 29 March 2024 Type: Research Article

Open Access

Received
1 November 2023

Accepted
1 March 2024

Published
29 March 2024

Abstract

The extensions of ordinary fuzzy sets are problematic because they require decimal numbers for membership, non-membership and indecision degrees of an element from the experts, which cannot be easily determined. This will be more difficult when three or more digits’ membership degrees have to be assigned. Instead, proportional relations between the degrees of parameters of a fuzzy set extension will make it easier to determine the membership, non-membership, and indecision degrees. The objective of this paper is to present a simple but effective technique for determining these degrees with several decimal digits and to enable the expert to assign more stable values when asked at different time points. Some proportion-based models for the fuzzy sets extensions, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets are proposed, including their arithmetic operations and aggregation operators. Proportional fuzzy sets require only the proportional relations between the parameters of the extensions of fuzzy sets. Their contribution is that these models will ease the use of fuzzy set extensions with the data better representing expert judgments. The imprecise definition of proportions is also incorporated into the given models. The application and comparative analyses result in that proportional fuzzy sets are easily applied to any problem and produce valid outcomes. Furthermore, proportional fuzzy sets clearly showed the role of the degree of indecision in the ranking of alternatives in binomial and trinomial fuzzy sets. In the considered car selection problem, it has been observed that there are minor changes in the ordering of intuitionistic and spherical fuzzy sets.

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Biographies

Kahraman Cengiz

kahramanc@itu.edu.tr

C. Kahraman graduated from Kuleli Military High School in 1983. He received his BSc degree in 1988, MSc degree in 1990, and PhD degree in 1996 from industrial engineering of Istanbul Technical University. Prof. Kahraman is now a full professor at Istanbul Technical University. His research areas are engineering economics, quality control and management, statistical decision making, multicriteria decision making, and fuzzy decision making. He published about 350 journal papers and about 250 conference papers. He became a guest editor of many international journals and an editor of many international books from Springer and Atlantis Press. He is the member of editorial boards of 20 international journals. He organized various conferences such as FLINS, RACR, FSSCMIE, and INFUS. He was the vice dean of ITU Management Faculty between 2004–2007 and the head of ITU Industrial Engineering Department between 2010–2013.

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Keywords

proportional fuzzy sets intuitionistic fuzzy sets Pythagorean fuzzy sets picture fuzzy sets spherical fuzzy sets

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