Deriving Fuzzy Inequalities Using Discrete Approximation of Fuzzy Numbers

Relative comparison of fuzzy numbers plays an important role in the domain of the fuzzy multi-criteria and multi-attribute decision making analysis. For making a comparison between two fuzzy numbers, beyond the determination of their order, the concept of inequality is no longer crisp. That is, an inequality becomes fuzzy in the sense of representing partial belonging or degree of membership when one makes a cardinal comparison between two or more hypothetical fuzzy numbers. It means that we need to calculate m ( ) in the fuzzy inequalities and among two normal fuzzy numbers. In this paper we propose a method for capturing the membership degree of fuzzy inequalities through discretizing the membership axis (?) into equidistant intervals. In this method, the two discretized fuzzy numbers are compared point by point and at each point the degree of preferences is identified. To show its validity, this method is examined against the essential properties of fuzzy number ordering methods in [Wang, X. and E.E. Kerre, Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets and Systems, 2001. 118(3): p. 375-385]. Furthermore it is compared numerically with some of the celebrated fuzzy number ranking methods. The results, which provides promising outcomes, may come in useful in the domain of fuzzy multi-criteria or multi-attribute decision making analysis, and more importantly, for fuzzy mathematical programming with fuzzy inequality constraints.