COMMUTATIVE IMPLICATIONS ON COMPLETE LATTICES

This paper is devoted to the investigation of commutative implications on a complete lattice L. It is proved that the disjunctive normal form (DNF) of a linguistic composition * is included in the conjunctive normal form (CNF) of that *, i.e., DNF(*) ≤ CNF(*) holds, for a special family of t-norms, t-conorms and negations induced by commutative implications.