Optimizing an unconstrained multi objective model using a utility based fuzzy probabilistic α-cut method

Abstract

Optimizing an uncertain multi-objective unconstrained mathematical model is proposed. One way to optimize multi objective mathematical models is to employ utility functions for the objectives. Recent studies on utility based multi objective optimization consider only one utility function for each objective. But, in reality it is not reasonable to have a unique utility function corresponding to each objective function. Here, an unconstrained multi objective mathematical model is considered in which several utility functions are associated for each objective. A fuzzy probabilistic approach is incorporated to investigate the uncertainty of the utility functions for each objective. Since these utility functions are uncertain and in fuzzy form, the total utility function of the problem is a fuzzy nonlinear mathematical model. While, there are not any conventional approaches to solve such a model, a defuzzification method to change the total utility function to a crisp nonlinear model is employed. Meanwhile, -cut method is applied to defuzzify the conditional utility functions. Then, an existing method to optimize the final single objective nonlinear model is adapted. The obtained results show that by changing the utility functions regarding to the dynamism of the environment, the method is still capable to provide the solutions accordingly. The effectiveness of the proposed approach is shown by solving a test problem.