Purpose-The purpose of this paper is to study the relationship between the property of distributivity and Zadeh's operators. Design/methodology/approach-The results are established by studying the relationship between the condition of distributivity and Zadeh's operations. Findings-When the tconorm T * and t-norm T are Zadeh' s "intersection"and "union" operations, respectively, or when the pseudo-addition % and pseudo-multiplication are Zadeh's "intersection" and "union"operations, respectively, a series of sufficient and necessary conditions for T * and T (or % and) to satisfy a distributivity property are obtained. These results are readily applied to emirings. Originality/value – New theoretical results are discovered and are shown to be useful to the study of triangular operators and applications in intelligent systems.