Abstract
The purpose of this paper is to provide a new method for solving the convexly combined form of composite fuzzy relation equations, λ·(x_??_R)+λ·(x_??_R)=y, for the two unknown fuzzy relations R, R in order to enhance the applicability of the convexly combined form of composite fuzzy relation equations to the modelling and identification of fuzzy input-output systems. The new method is to find the maximin solution, (R*, R*), of the convexly combined form of composite fuzzy relation equations, λ·(x_??_R)+λ·(x_??_R)=y, where x and y are the given fuzzy sets, λ is the given fuzzy convex combinator whose complement is λ, R and R are the unknown fuzzy relations, and the symbols “_??_”, “_??_”, “·”, “+” denote the sup·min composition, inf·max composition, algebraic product, algebraic sum respectively.
