Generating pseudo-t-norms and implication operators.

*(English)*Zbl 1085.03020Summary: 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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