Transitive coupling for fuzzy system matrices

The problem presently solved is interconnecting two multilevel fuzzy subsystem models defined by fuzzy matrices A and B, and a common, transitive, fuzzy relation to form a fuzzy system model defined by fuzzy matrix M. This problem is called a fuzzy transitive coupling. The entries of the unknown interconnection matrices X and Y are shown to form multilevel implication structures. The implication structures in transitive coupling of fuzzy system models are analyzed. Effective generation algorithms of implication matrices are proposed. Algorithms for assignment to unknowns are obtained. Using the implication matrix models, the fuzzy transitive coupling can be efficiently performed