An algorithm for minimizing a linear objective function subject to the fuzzy relation inequalities with addition–min composition

In this paper, we study the optimal solution of minimizing a linear objective function subject to the fuzzy relation inequalities with addition–min composition. We first discuss some properties about the minimal solutions of fuzzy relation inequalities with addition–min composition, and define the pseudo-minimal indexes of this system. Next we give an algorithm to get the set of the pseudo-minimal indexes, which is called PMI algorithm. Finally, we obtain an algorithm for this optimization system by utilizing these concepts and results. The example is provided to show that our algorithm is simple and convenient.