Minimizing a linear function under a fuzzy max-min relational equation constraint

In this paper we investigate the problem of minimizing a linear objective function subject to a fuzzy relational equation constraint. A necessary condition for optimal solution is proposed. Based on this necessary condition, we propose three rules to simplify the work of computing an optimal solution. Numerical examples are provided to illustrate the procedure. Experimental results are reported showing that our new procedure systematically outperforms our previous work.