Weakly associative functions on [0, 1] as logical connectives [fuzzy logic]

This report focuses on a property of conjunctive operators named "weak associativity," which is one of sufficient conditions for the syllogism in fuzzy logic. The authors introduce a class of binary operators on [0, 1], which satisfy the weak associativity and some boundary conditions. Our newly introduced class is broader than the class of t-norms, and is included in that of Galois-operators on [0, 1], which, and of which, the right-residuals form Galois-connections on [0, 1]. In addition, the authors show some methods to construct some weakly associative functions by using the generators of t-norms.