A Fuzzy Probabilistic Maximum Technique to Optimize an Unconstrained Utility Based Multi Objective Model
- *Corresponding Author:
- Hamed Fazlollahtabar
Faculty of Industrial Engineering
Iran University of Science and Technology
Tel: +98 21 7724054
E-mail: [email protected]
Received date: November 14, 2014; Accepted date: December 22, 2014; Published date: January 15, 2015
Citation: Torkjazi M, Fazlollahtabar H (2015) A Fuzzy Probabilistic Maximum Technique to Optimize an Unconstrained Utility Based Multi Objective Model. Ind Eng Manage 3:147. doi:10.4172/2169-0316.1000147
Copyright: © 2015 Torkjazi M, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
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, maximum technique 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.