Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
396103 | Information Sciences | 2007 | 12 Pages |
Abstract
This paper deals with a general α -decomposition problem of fuzzy relations, which can be stated as follows: given a fuzzy relation R∈F(X×Y)R∈F(X×Y), determine two fuzzy relations Q∈F(X×Z)Q∈F(X×Z) and T∈F(Z×Y)T∈F(Z×Y) such that R=QαT, where X (resp. Y) is a finite set. Firstly we point out that every fuzzy relation R is always generally α-decomposable, and give an algorithm to construct Q and T with R=QαT for a given R . Secondly, we show that the general content ρ(R)ρ(R) with ρ(R)=min{|Z|:R=QαT,Q∈F(X×Z),T∈F(Z×Y)} is equal to the chromatic number of the simple graph FR generated by R . Therefore, finding an exact algorithm for calculating ρ(R)ρ(R) is an NP-complete problem.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Yan Yang, Xue-ping Wang,