Penalized Intuitionistic Fuzzy Goal Programming Method for Solving Multi-Objective Decision-Making Problems

Many applicable problems have multi-goals that optimize simultaneously, and decision-makers set imprecise aspiration levels for each goal. Although such types of problems solved by fuzzy optimization are common in the literature, intuitionistic fuzzy optimization techniques are more efficient to handle than fuzzy and classical optimization. This research study focused on establishing a novel method by combining the penalty function method with an interactive goal programming methodology for addressing multi-objective decision-making problems in an intuitionistic fuzzy environment. One of the challenge that exists in the literature of the optimization method under an imprecise decision environment is that it is not guaranteed to generate a Pareto-optimal solution for the introduced problem. Therefore, in order to ensure the Pareto-optimality of the obtained solution, the suggested method has developed a new aggregation operator, an appropriate relaxation of the constraint set, and a well-structured extended Yager membership function. In addition, unlike other methods in the literature, the suggested method gives decision-makers the option to penalize the most unsatisfied objective function at a specific attained solution instead of starting from scratch and working their way through the problem. To illustrate the proposed method, we used a numerical example.