An intuitionistic fuzzy goal programming approach for finding pareto-optimal solutions to multi-objective programming problems

Multi-objective optimization in the intuitionistic fuzzy environment is the process of finding a Pareto-optimal solution that simultaneously maximizes the degree of satisfaction and minimizes the degree of dissatisfaction of an intuitionistic fuzzy decision. In this paper, a new method for solving multi-objective programming problems is developed that unlike other methods in the literature, provides compromise solutions satisfying both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. This method combines the advantages of the intuitionistic fuzzy sets concept, goal programming, and interactive procedures, and supports the decision maker in the process of solving programming problems with crisp, fuzzy, or intuitionistic fuzzy objectives and constraints. A characteristic of the proposed method is that it provides a well-structured approach for determining satisfaction and the dissatisfaction degrees that efficiently uses the concepts of violation for both objective functions and constraints. Another feature of the proposed method comes from its continuous interaction with the decision maker. In this situation, through adjusting the problem's parameters, the decision maker would have the ability of revisiting the membership and non-membership functions. Therefore, despite the lack of information at the beginning of the solving process, a compromise solution that satisfies the decision maker's preferences can be obtained. A further feature of the proposed method is the introduction of a new two-step goal programming approach for determining the compromise solutions to multi-objective problems. This approach ensures that the compromise solution obtained during each iterative step satisfies both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The application of the proposed model is also discussed in this paper.