A CLASS OF FUZZY MEASURES BASED ON TRIANGULAR NORMS A general framework for the combination of uncertain information

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Abstract
An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short). Fuzzy measures are actually set functions which are monotonic with respect to set inclusion. Triangular norms and conorms are semi-groups of the unit interval which have been thoroughly studied in the literature of functional equations. The proposed class encompasses probability measures, Zadeh's possibility measures and the dual notion of necessity measures. Any set function of the class can be expressed in terms of a density, and constructively defined out of this density. This feature makes the proposed framework attractive from a practical point of view for the representation and manipulation of subjective evidence. The link between t-norm and t-conorm based set functions and Shafer's belief functions is invesligaled.

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