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Closure properties of the compositional rule of inference. (English) Zbl 0704.03006
Author’s abstract: “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 $$\chi_ P$$, $$\chi_ Q$$ and $$\chi_ R$$ from a certain class of functions C. It is shown that when the parameters of these three functions are chosen equal, then either $$\chi_ P$$, $$\chi_ Q$$ and $$\chi_ R$$ are the same, or $$\chi_ Q$$ lies between $$\chi_ P$$ and $$\chi_ R$$. In this case it can be shown where approximately $$\chi_ Q$$ lies between $$\chi_ P$$ and $$\chi_ R$$. Unfortunately its position depends on the original parameters of $$\chi_ P$$ and $$\chi_ R$$.”
Reviewer: S.Rudeanu

##### MSC:
 03B52 Fuzzy logic; logic of vagueness
##### Keywords:
compositional rule of inference
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