A bayesian functional approach to fuzzy system representation

In the present contribution, we develop a fuzzy function representation based on a probabilistic approach to fuzzy sets — the likelihood sets. Fuzzy functions, rather than fuzzy sets, are placed in the center of the fuzzy paradigm. Fuzzification, inference, defuzzification stages are naturally established as results deriving from bayesian estimation theory. Some important problems such as fuzzy system prediction and model inversion are addressed in this framework and some results are presented. The input-output behavior of a fuzzy system is an interpolating scheme with a symbolic specification given in terms of fuzzy logic. The formulation of the semantic framework for the fuzzy systems we develop here provides suitable way to deal with the introduction of a priori information — expressed in a qualitative way.