On modeling a lexicographic weighted maxmin–minmax approach for fuzzy linear goal programming

In this paper, a novel approach for solving fuzzy goal programming is proposed.  This approach utilizes the weighted maxmin and weighted minmax methods simultaneously.  Relative weight is assigned to each fuzzy goal according to the preference of the decision maker.  A model for each of the two methods is separately stated; hence the two models are merged into one.  Moreover, the lexicographic maximization technique is applied to guarantee efficient solutions.  Therefore, the proposed approach allows the decision maker to compromise between the two methods.  Furthermore, the proposed approach can be implemented to concave piecewise linear membership functions.  This type of membership function is represented using the min-operator.  The effectiveness of the proposed approach is illustrated by a numerical example.