CLOSURE-PROPERTIES OF THE COMPOSITIONAL RULE OF INFERENCE

This paper deals with the compositional rule of inference: if x is P and x and y are R, then y is Q, where Q is defined in terms of P and R. P, Q and R are fuzzy sets defined with membership functions χP, χQ and χR from a certainclass of functions C. It is shown that when the parameters of these three functions are chosen equal, then either χP, χQ and χR are the same, or χQ lies between χP and χR. In this last case it can be shown where approximately χQ lies between χP and χR. Unfortunately its position depends on the original parameters of χP and χR. © 1990.