Element selection from a fuzzy subset using the fuzzy integral

The problem of selecting a crisp element based upon a fuzzy set is investigated. It is noted that the defuzzification problem in fuzzy logic control is a special case of this problem. The given fuzzy subset is considered as a set of pieces of advice where the strengths of the advice is the membership grade. This problem is formulated in terms of a generalized expected value, an aggregation problem, by using the fuzzy integral. Ways to convert the fuzzy set into a fuzzy measure are shown. Different structures for the calculation of best action are developed