On Zadeh’s Compositional Rule of Inference
نویسندگان
چکیده
This paper deals with Zadeh’s compositional rule of inference [12] under triangular norms: IF X is P AND X and Y have relation R, THEN Y is Q, where P and Q are fuzzy sets of the real line IR, R is a fuzzy relation on IR and the conclusion Q is defined via sup-T composition of P and R: μQ(y) = sup x∈IR T (μP (x), μR(x, y)), y ∈ IR. It is shown that (i) when the triangular norm T and the membership function of the observation P are continuous, then the conclusion Q depends continuously on the observation; (ii) when T and the membership function of the relation R are continuous, then the observation Q has continuous membership function. Furthermore, we present similar results for the discrete case and for multiple fuzzy reasoning schemes.
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