Ranking triangular interval-valued fuzzy numbers based on the relative preference relation

Abstract

In this paper, we first use a fuzzy preference relation with a membership function representing preference degree forcomparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzypreference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total orderingrelation that satisfies reciprocal and transitive laws on interval-valued fuzzy numbers, the relative preference relation isalso a total ordering relation. Practically, the fuzzy preference relation is more reasonable on ranking interval-valuedfuzzy numbers than defuzzification because defuzzification does not present preference degree between fuzzy numbersand loses messages. However, fuzzy pair-wise comparison for the fuzzy preference relation is more complex and difficultthan defuzzification. To resolve fuzzy pair-wise comparison tie, the relative preference relation takes the strengths ofdefuzzification and the fuzzy preference relation into consideration. The relative preference relation expresses preferencedegrees of interval-valued fuzzy numbers over average as the fuzzy preference relation does, and ranks fuzzy numbersby relative crisp values as defuzzification does. In fact, the application of relative preference relation was shown intraditional fuzzy numbers, such as triangular and trapezoidal fuzzy numbers, for previous approaches. In this paper, weextend and utilize the relative preference relation on interval-valued fuzzy numbers, especially for triangular intervalvalued fuzzy numbers. Obviously, interval-valued fuzzy numbers based on the relative preference relation are easily and quickly ranked, and able to reserve fuzzy information.