On the maximum entropy parameterized interval approximation of fuzzy numbers

This paper extends the interval-valued weighted possibilistic mean of a fuzzy number of Fullér and Majlender to a general weighting function without the monotonic increasing assumption. This weighting function determines a weighted average aggregation of the cuts of the fuzzy number according to the preference of a decision-maker. Some properties of the weighting function are provided and a preference index that qualifies this aggregation and can serve as a parameter for the definition of interval approximation of a fuzzy number is proposed. A special class of parameterized weighting functions satisfying the maximal entropy principle is proposed.