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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
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