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.
Keywords
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
Publisher
:Emerald Group Publishing Limited
Copyright © 2006, Emerald Group Publishing Limited