A New Method For Ranking Interval Type-2 Fuzzy Numbers Based On Mellin Transform

Interval type-2 fuzzy sets provide us with additional degrees of freedom to represent the uncertainty and the fuzziness of the real word than traditional type-1 fuzzy sets. Interval type-2 fuzzy numbers ranking has an important role in the decision making analysis. In this paper, the probatilistic mean value and variance of interval type-2 fuzzy numbers are proposed based on the Mellin transform for type-1 fuzzy numbers. The interval type-2 fuzzy number with the higher mean is ranked higher. If the mean values are equal the one with the smaller variance is judged higher rank. On this basis, some new distance measures and possibility degree formula are proposed to comparing interval type-2 fuzzy numbers based on their Mellin mean value and variance. Some benchmarking numerical examples are given, and some interpretation issues are explained.