Review and Comparison of Bipolar Fuzzy Number Types.

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.