ABSTRACT
However, to formulate a realistic problem as a mathematical optimization model, the decision-maker often encounters the situation of hesitation and vagueness in deciding the values of the input parameters. To enrich the optimization theory under uncertainty, the notion of fuzzy sets was further extended to the intuitionistic fuzzy sets which associates a rejection degree along with the acceptance degree for each element of the set. Later on, several authors devised different techniques to solve the various optimization problems under a fuzzy environment. Ammar explored the fuzzy random multi-objective QPPs, and thereby, solved a portfolio optimization problem. Motivated by the IF approach given by Angelov to solve the optimization models, the proposed methodology uses and cuts for the objective function and the constraints to reduce the original IF-QPP to two subproblems giving the lower bound and upper bound for the objective value.
