Resolution of fuzzy relation equations (I) based on boolean-type implications

The problem of solving fuzzy relation equations (I) based on Boolean-type implications is studied in the present paper. Decomposition of fuzzy relation equations (I) based on Boolean-type implications is presented in a finite case. The solution existence of fuzzy relation equations (I) based on Boolean-type implications is studied, and for nice Boolean-type implications, some new solvability criteria based upon the notion of “solution matrices” are discussed. The complete solution set of fuzzy relation equation (1) based on Boolean-type implication can be determined by the maximal solution set of this equation, which is finite. An effective method to solve fuzzy relation equations (I) based on Boolean-type implications is proposed.