Review and Comparison of Bipolar Fuzzy Number Types.

Document Type : Review article

Authors

Department of Mathematics, Gonbad Kavous University,, Gonbad Kavous, Iran

Abstract

Many human decision-making processes such as competition, hostility, partnership, etc. are based on bipolar or two-sided thinking, which are positive on one side and negative on the other. Binary logic only includes zero and one, and fuzzy logic is a tool for representing ambiguity and uncertainty, but both have shortcomings in modeling bipolar relationships, as they are limited to the range from zero to one, which is suitable for representing unipolar models in nature. Bipolar fuzzy sets are actually a combination of ambiguity and its polarity, which is a tool for representing subjects of nature that have both positive or negative poles. Therefore, in this article, we will introduce bipolar fuzzy sets and numbers, and then, by defining addition and scalar multiplication for triangular bipolar fuzzy numbers, we will introduce a new ranking based on the centroid for this category of numbers, and prove the properties of the new method by stating several theorems and propositions. Finally, numerical examples demonstrate the practical applications of the proposed ranking.

Keywords

Main Subjects

References

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Fuzzy Systems and its Applications
Volume 6, Issue 2 - Serial Number 13
January 2024
Pages 91-113

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History

  • Receive Date: 11 May 2023
  • Revise Date: 19 October 2023
  • Accept Date: 06 December 2023

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