An Extended Necessity Measure Maximisation Incorporating the Trade-Off between Robustness and Satisfaction in Fuzzy LP Problems

Abstract

When some coefficients of the constraints are uncertain with only their possible ranges being given, a conventional linear programming (LP) problem can be generalised to the one with set-inclusive constraints. We consider the case where the possible ranges are given by fuzzy sets in this paper. The set-inclusive constraints with fuzzy coefficients have been treated by a necessity measure. However, the usual necessity measure cannot express well the decision-maker’s requirement about the trade-off between the robustness level and the satisfaction level of the constraints. We extend the necessity measure to incorporate the trade-off between the robustness level and the satisfaction level of the constraints. We apply the extended necessity measure to LP problems with fuzzy coefficients. After the problem is formulated and reduced to the conventional programming problem, we propose a solution algorithm. Numerical examples are given to illustrate the proposed approach.