Ranking fuzzy numbers with preference weighting function expectations

Based on the recent research developments of fuzzy number ranking, the paper extends the centroid expectation approach and proposes a preference weighting function expectation method to rank fuzzy numbers. The weighting function gives different emphasis on the possible values of the fuzzy number, which can be used to represent the decision makerʹs pessimistic, neutral, or optimistic attitude. An optimistic measure to represent this preference information is proposed. Some properties of the weighting function and optimistic measure are systematically analyzed. Then, the paper proposes a special class weighting function with maximum entropy principle and analyzes some of its properties. With this parameterized maximum entropy weighting function, we can get preference expectation of any fuzzy number with given optimistic level. Next, the weighting function is extended to represent the confidential attitude of the decision maker by giving different emphasis on the cut level set of the fuzzy number. Some results about confidential attitude that parallel to the valuation attitude are attained. We especially extended the BADD (basic defuzzification distribution) approach with preference expectation of fuzzy numbers, and another confidential measure with BADD operator is proposed. Finally, the expected valuations of fuzzy numbers are used to ranking the fuzzy numbers. Compared with other fuzzy number ranking methods, the method of this paper is easily interpreted, robust, flexible, and invariant with translating and scaling for real numbers.