An Algebraic Structure of Fuzzy Logics with Weakly Associative Conjunctors

This research focuses on an algebraic structure of fuzzy logics equipped with weakly associative conjuctors. The authors show that the weak associativity of conjunctors should reduce to the associativity in such algebras with one conjuctor and two implicators as the conventional non-commutative fuzzy logics. As the main result of this article, we give the definition of an algebra equipped with one implicator and two weakly associative conjunctors.