A NOTE ON 'DECOMPOSITION PROBLEM OF FUZZY RELATIONS'

摘要

The decomposition problem of a fuzzy relation R∈F(X×X) can be stated as :"Given a fuzzy relation R∈F(X×X), to determine whether there exists a fuzzy relation Z∈F(X×X) such that R=Z⊙Z, where X is a finite set and "⊙" is the max-min com- Position of two fuzzy relations." In particular, if R is a Boolean matrix, then this prob- Lem becomes to find the square root of a Boolean matrix, which is a well-known Unsolved problem.