Parameterized defuzzification with maximum entropy weighting function—Another view of the weighting function expectation method

This paper mainly extends the weighting function expectation method from fuzzy numbers to the ordinary fuzzy set, and regards it as a weighting function defuzzification method. Some properties are discussed in the defuzzification context. The traditional center of gravity (COG) defuzzification method is extended to the weighting function COG (WFCOG) defuzzification method, which can represent the decision maker’s subjective attitude. With the properties of the weighting function, a parameterized defuzzification method with maximum entropy weighting function is proposed. Then it is integrated with the basic defuzzification distribution (BADD) method, which can represent the decision maker’s valuation and confidential attitude respectively. The relationships between the weighted function BADD defuzzification method and some existing defuzzification methods are discussed. The COG, MOM (mean of maxima), FOM (first of maxima), LOM (last of maxima), MOS (mean of support), FOS (first of support), and LOS (last of support) all become special cases with specific valuation and confidential attitude parameters.