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Van Melle’s combining function in MYCIN is a representable uninorm: An alternative proof. (English) Zbl 0928.03060
Summary: Recently, A. Tsadiras and K. Margaritis [ibid. 93, 263-274 (1998)] have shown that the function implemented in the expert system MYCIN for combining certainty factors is a uninorm. In this paper, we present a compact alternative to the given direct and lengthy proof, based on the construction of representable uninorms by means of an additive generator. Consequently, we show that van Melle’s combining function is a representable uninorm. In fact, it is a rescaled version of the representable uninorm on the unit interval constructed from the algebraic product and the probabilistic sum.

MSC:
03E72 Theory of fuzzy sets, etc.
68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
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