Abstract
Abstract The aim of this paper is to provide a close upper bound of the membership function for the compositional rule of inference under Archimedean t-norm, where both the observation and the relation parts are given by Hellendoorn's φ-function (1980). In particular, if the left and right spreads of the observation part is the same as those of the relation part, then this upper bound is the exact membership function, which generalizes the earlier result by Fuller and Zimmermann (1982) in that assumption of twice differentiability is deleted.
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