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 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.