An Efficient Approach for the Optimization of Fuzzy Relation Equations with Max-min Composition

摘要

In literature, optimization model with a linear objective function subject to fuzzy relation equations using max-min composition has been converted into a 0-1 integer programming problem by Fang and Li. They first reduced the problem by exploring the special structure of the problem and solved by a branch-and-bound method! In this paper, we shall focus on the characterization of optimal solution. With the help of this characterization, we derive a value matrix and present some rules to reduce the problem. An upper bound for the optimal objective value of the reduced problem will be presented. Based on this upper bound, the problem may be reduced further by our rules. Numerical example is provided to illustrate our scheme. Furthermore, our example shows that with the help of our rules and upper bound the optimal solution can be easily obtained to solve the problem without invoking the branch-and-bound method. Numerical experiments also show that the performance of our scheme is superior to the procedure in Fang and Li and accelerated Fang and Li's method.