The Solution Sets Of @-Fuzzy Bilinear Equations On [0,1] And The σ-decomposition Of A Fuzzy Relation R

In this paper, we deal with the solution sets of @-Fuzzy bilinearequations on [0,1] and theσ-decomposition of a fuzzy relation R. In par-ticular, we deal with the finite @-Fuzzy bilinear equations on [0,1]. Someproperties of @-fuzzy bilinear equations are given, then the solution sets andthe result associated with the solution sets of @-fuzzy bilinear equations areobtained. Further, we deal with the infinite @-Fuzzy bilinear equations on[0,1]. Some properties of @-fuzzy bilinear equations are given, then whenX = and G(r) = , the solution sets are obtained. In the end, we dealwith theσdecomposition problem of a fuzzy relation R on [0,1] . First,a necessary and sucient condition that a fuzzy relation R isσdecom-posable is given. Then the solution sets of A and B with AσB = R are obtained.