Solving interval-valued fuzzy relation equations

From the algorithm procedure presented in section 4 and the examples in this section, we can nd out it is easy to solve interval valued fuzzy relation equations by using fuzzy relation inequality system (8). The computation complexity of this algorithm is as same as that of the more commonly used algorithm 5] for fuzzy relation equations (1). So, the problem is more complicated than constant fuzzy relation equations, but the computation complexity of algorithm is the same. Of course, because of the non-convex characteristic of solution set of problem (2), it is not a polynomial-time algorithm. 6 Conclusion In this paper we have presented a computational procedure to generate the whole solution set of a system of interval valued fuzzy relation equations. The basic idea of the proposed algorithm is to change the interval valued fuzzy relation equations into a fuzzy relation inequality system. By nding the maximum solution rst, then the minimum ones, we can determine the whole solution set.