Evaluation of fuzzy quantities by means of a weighting functions

We consider here fuzzy quantities, i.e. fuzzy sets without any hypothesis about normality nor convexity. Two main topics are examined: the first one consists in defining the evaluation of a fuzzy quantity, in such a way that it may be applied both in ranking and in defuzzification problems. The definition is based on α-cuts and depends on two parameters: a coefficient connected with the optimistic or pessimistic attitude of the decision maker and a weighting function similar to a density function. The second aim is showing that the proposed definition is suitable for defuzzifying the output of a fuzzy expert system: we treat a classical example discussed in [1], using several t-norms and t-conorms in aggregation procedures.