Distributivity and Zadeh's operators

Abstract

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 ⊕ 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 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.

Citation

Tong, X., Li, H., Chen, M. and Lin, Y. (2006), "Distributivity and Zadeh's operators", Kybernetes, Vol. 35 No. 10, pp. 1628-1635. https://doi.org/10.1108/03684920610688612