Interval Goal Programming Approach to Multiobjective Fuzzy Goal Programming Problem with Interval Weights

This article presents interval goal programming (IGP) approach for solving linear multiobjective fuzzy goal programming problem with interval weights. In the proposed approach, interval weights for achievement of fuzzy goals to their aspired levels on the basis of their relative importance are considered in an uncertain environment. In the model formulation of the problem, the membership functions for each of the fuzzy goals are defined first. Then, the membership functions are transformed into membership goals by assigning the highest membership value (unity) and introducing under-and over-deviational variables to each of them. In the solution process, the interval weights (derived from pairwise interval judgment matrix) associated with the unwanted deviational variables is introduced in the goal achievement function for minimizing them to reach the aspired goal levels of the problem. To illustrate the proposed approach, a numerical example is solved.