TARSKI’s FUZZY CONSEQUENCES
نویسنده
چکیده
The aim of this paper is to prove that the following two mathematical concepts are equivalent: 1) Fuzzy Preorders which are compatible with an "AND" operation and 2) Fuzzy Consequence Operators (FCO) [8] verifying a finiteness property with respect to that "AND" operation. The role proposed to fuzzy consequences operators is to be a general notion for obtaining approximate consequences from approximate premises [6,8]. So, this paper justifies the use of fuzzy preorders to model the deductive closure of a rule base, as it is made in many Expert Systems [7]. Moreover, as a corollary of this result, we have that all FCOs verifying the finite condition mentioned before are axiomatizable using only the rule of multiple valued Modus Ponens and an appropriate set of logical implications as axioms.
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