A joint maxmin-lexicographic maximisation approach in fuzzy goal programming using dominance possibility and necessity criteria

Abstract

In this paper, a new approach for solving fuzzy goal programming problems is introduced. The coefficients and the aspiration level of each fuzzy goal are considered either trapezoidal or triangular fuzzy numbers. Four dominance criteria (dominance possibility, strict dominance possibility, dominance necessity, and strict dominance necessity) are utilised for comparing the fuzzy numbers. The proposed approach is based on merging the maxmin approach and the lexicographic approach in a two-phase process. The first phase applies the maxmin technique by maximising the minimum achievement degree of the fuzzy goals. The second phase lexicographically maximises the achievement degrees of the fuzzy goals according to their preemptive priorities. This methodology provides the decision maker with the advantage of improving the results of his preemptive priority structure model by initially maximising the lowest achievement of the fuzzy goals, and hence guarantee that the ultimate achievement of any fuzzy goal will never be lower than a specific percentage of the achieved maxmin value. The suggested approach is illustrated by a numerical example.