An algorithm for solving fuzzy relation equations with max-T composition operator

This paper studies the problem of solving a max-T composite finite fuzzy relation equation, where T is a special class of pseudo-t-norms. If the equation is solvable, then its set of feasible solutions is determined by the greatest solution and a finite number of minimal solutions. Some necessary conditions are presented for the minimal solutions in terms of the maximum solution and zero value. Under these conditions, some minimal solutions of the system can be obtained easily. Some procedures are also proposed in order to simplify the original system. The simplified system is then decomposed (if possible) into several subsystems with smaller dimensions, which are very easy to solve. Furthermore, a method is presented to solve each subsystem. By combining the method and those procedures, an efficient algorithm is proposed to obtain the set of feasible solutions of the original system. Two examples are also given to illustrate the algorithm.