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Generating pseudo-t-norms and implication operators. (English) Zbl 1085.03020
Summary: In this paper, we show that the set of all pseudo-t-norms, the set of all implications, the set of all infinitely $$\vee$$-distributive pseudo-t-norms, and the set of all infinitely $$\wedge$$-distributive implications on a complete Brouwerian lattice are all complete lattices and lay bare the formulas for calculating the smallest pseudo-t-norm (the smallest infinitely $$\vee$$-distributive pseudo-t-norm) that is stronger than a binary operation and the largest implication (the largest infinitely $$\wedge$$-distributive implication) that is weaker than a binary operation.

MSC:
 03B52 Fuzzy logic; logic of vagueness
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References:
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