Applying a utility based fuzzy probabilistic αα-cut method to optimize a constrained multi objective model

This article is proposing an appropriate approach to solve a constrained multi objective model by using the theory of utility functions in fuzzy form. One of the approaches to optimize a multi objective mathematical model is to employ utility functions for the objectives. Recent studies on utility based multi objective optimization concentrate on considering just 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, a constrained multi objective mathematical model is considered in which several utility functions are associated for each objective. All of these utility functions are uncertain and in fuzzy form, so a fuzzy probabilistic approach is incorporated to investigate the uncertainty of the utility functions for each objective and the total utility function of the problem will be a fuzzy nonlinear mathematical model. Since 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, αα-cut method is applied to defuzzify the conditional utility functions. This action results in changing the total utility function to a crisp single objective nonlinear model and will simplify the optimization process of the total utility function. The effectiveness of the proposed approach is shown by solving a test problem.