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Pseudo-t-norms and implication operators on a complete Brouwerian lattice. (English) Zbl 1013.03020
Fuzzy Sets Syst. 132, No. 1, 113-124 (2002); corrigendum ibid. 153, No. 2, 295-296 (2005).
Given a complete Brouwerian lattice \(L\), a pseudo-t-norm is a binary operation \(T\) on \(L\) such that \( T(1,a) = a \), \(T(0,a) = 0 \) and \( T(a,b) \leq T(a,c)\) whenever \( b \leq c\). Motivated by problems of fuzzy logic, the authors extend previous works on relations between t-norms and implication functions. More precisely, they study in detail the relations between the set of all infinitely \(\vee\)-distributive pseudo-t-norms and the set of all infinitely \( \wedge\)-distributive implications on \(L\). Some examples and particular cases are presented. [See also the notes on this article in the same journal 153, No. 2, 289-294 (2005; Zbl 1086.03019).]

MSC:
03B52 Fuzzy logic; logic of vagueness
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