A general defuzzification method for a fuzzy system output depending on different T-norms

We consider here fuzzy quantities, i.e., fuzzy sets without any hypothesisabout normality nor convexity. Two main topics are examined: the firstone consists in defining the evaluation of a fuzzy quantity, in such a waythat it may be applied both in ranking and in defuzzification problems.The definition is based on α-cuts and depends on two parameters: acoefficient connected with the optimistic or pessimistic attitude of thedecision maker and a weighting function similar to a density function. Thesecond aim is showing that the proposed definition is suitable fordefuzzifying the output of a fuzzy expert system: we treat a classicalexample discussed in [2], using several t-norms and t-conorms inaggregation procedures.