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This report focuses on a property of conjunctiveoperators named "weak associativity," which is one ofsufficient conditions for the syllogism in fuzzy logic. Theauthors introduce a class of binary operators on [0,1]which satisfy the weak associativity and some boundaryconditions. Our newly introduced class is broader than theclass of t-norms, and is included in that of Galois-operatorson [0,1] , which and of which right-residuals formGalois-connections on [0,1] . In addition, the authorsshow some methods to construct some weakly associativefunctions by using the generators of t-norms.