Resolution of finite fuzzy relation equations based on strong pseudo-t-norms Original Research Article

This work studies the problem of solving a sup-TT composite finite fuzzy relation equation, where TT is an infinitely distributive strong pseudo-t-norm. A criterion for the equation to have a solution is given. It is proved that if the equation is solvable then its solution set is determined by the greatest solution and a finite number of minimal solutions. A necessary and sufficient condition for the equation to have a unique solution is obtained. Also an algorithm for finding the solution set of the equation is presented.