Distributivity and Zadeh's operators

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 t-conorm T* and t-norm T are Zadeh's "intersection" and "union" operations, respectively, or when the pseudo-addition circle plus and pseudo-multiplication circle times are Zadeh's "intersection" and "union" operations, respectively, a series of sufficient and necessary conditions for T* and T (or circle plus and circle times) to satisfy a distributivity property are obtained. These results are readily applied to semirings. Originality/value - New theoretical results are discovered and are shown to be useful to the study of triangular operators and applications in intelligent systems.