Lexicographic optimal solution of the multi-objective programming problem subject to max-product fuzzy relation inequalities

It is shown in this paper that the emission base stations in wireless communication can be reduced into a system of fuzzy relation inequalities with max-product composition. For optimal management in such system, we introduce the fuzzy relation multi-objective programming. Concept of feasible index set (FIS) is defined, based on which a novel algorithm, named FIS algorithm, is developed to find the unique lexicographic optimal solution of the proposed problem with polynomial computational complexity. Applying this method, we needn't to find out all the minimal solutions of the constraint. A numerical application example is provided to illustrate the feasibility and efficiency of the FIS algorithm.