Approach for uncertain multi-objective programming problems with correlated objective functions under C_(EV) criterion

作     者：MENG Xiangfei WANG Ying LI Chao WANG Xiaoyang LYU Maolong 

作者机构：Equipment Management and Unmanned Aerial Vehicle Engineering College Air Force Engineering University Satellite Control CenterXi’an 

出 版 物：《Journal of Systems Engineering and Electronics》 (系统工程与电子技术（英文版）)

年 卷 期：2018年第29卷第6期

页      面：1197-1208页

核心收录：

学科分类：07[理学] 08[工学] 

基　　金：supported by the National Natural Science Foundation of China(71601183 71571190) 

主　　题：uncertainty theory uncertain multi-objective programming expected-variance value criterion 

摘      要：An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world ***, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain ***, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.