A Study on Fully Interval Valued Intuitionistic Fuzzy Multilevel Quadratic Programming Problem

Uncertainty is a parameter in optimization problems encountered in real-world scenarios. Identifying a particular category of models for multilevel linear programming under uncertainty is challenging. The emphasis of this research is the examination of uncertainty in multilevel quadratic programming problems. The primary aim of this initiative is to address the FIVIFMQP problem, which denotes completely interval-valued intuitionistic fuzzy multilevel quadratic programming. To convert the specified quadratic objective function into an equivalent linear objective, initially employ a linearization technique on the objective function. The anticipated value function is utilized for all elements of the objective function and constraints to derive an equivalent crisp model. The crisp model is subsequently resolved utilizing an augmented fuzzy methodology grounded in the anticipated value function. Resolving the multilevel programming problem can yield a compromise solution to the FIVIFMQP challenge. A numerical example is included to enhance comprehension of the solution approach of the proposed method.