Sets Of The Solution-set-invariant Coefficient Matrices Of Fuzzy Relation Equations

This paper investigates the coefficient matrices of solution invariant equa-tions assigned on [0,1]. First, it introduces the definition of fuzzy relational equations with max-* composition, i.e., Aox=b. Then, it gives the definition and some properties of the covering matrix for A o x=b. Next, it obtains the sufficient condition that the poset of coefficient matrices of solution invariant equations to A o x=b forms a lattice according to the covering matrices. In the end, this paper uses the characteristic matrices for the great-est solution and lower solutions to describe a set of solution-set-invariant coefficient matrices of the fuzzy relation equation with max-min composition, i.e., A ⊙ x=b, and it shows an algorithm for describing the set completely.