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Theory of T-norms and fuzzy inference methods. (English) Zbl 0726.03017
The notions of T-norm, T-conorm and a negation (N-) operator are reviewed. These are the operations that can correspond to &, \(\vee\) and \(\neg\) in fuzzy logic. The main operators that have been proposed are given and their properties are analyzed. All these operators can be used instead of min and max in all the applications of fuzzy logic (and in many applications they are better than max and min). In particular, the authors describe how these operators can be used in fuzzy reasoning: if we have several rules A,B\(\to C\); D,E,F\(\to C;...\), and we know the truth values \(\mu\) (A), \(\mu\) (B),... of A, B, D, E, F, then we can compute the resulting truth value of C as \(T^*(T(\mu (A),\mu (B)),T(\mu (D),\mu (E),\mu (F)),...),\) where \(T^*\) is a T-conorm (corresponding to \(\vee)\), and T is a T-norm (that corresponds to &). As a particular application of this general approach the authors consider fuzzy control.

MSC:
03B52 Fuzzy logic; logic of vagueness
93C42 Fuzzy control/observation systems
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