Coimplicators, the forgotten connectives. (English) Zbl 0954.03029

Summary: Triangular norms and conorms are generally considered as the most important conjunctors and disjunctors in fuzzy logic. Another interesting class of fuzzy logical connectives, often used in approximate reasoning, is the class of implicators. It is well known that triangular norms and conorms come in dual pairs. The dual operators of implicators, however, are hardly ever discussed. These dual operators called coimplicators, are the subject of this paper. In particular, border and model coimplicators on a bounded ordered set are introduced and studied. It is shown that any model coimplicator is uniquely determined by a triangular norm and an involutive negator. Furthermore, applying the technique of residuation, it is shown that to any triangular conorm on a complete lattice there corresponds a border coimplicator, called its residual coimplicator.


03B52 Fuzzy logic; logic of vagueness