Efficient Solutions for Uncertain Random Multiobjective Programming Problem

Based on the chance theory, which is founded for modeling complex systems with not only uncertainty but also randomness, this paper is devoted to studying a new kind of multiobjective programming problem where randomness and uncertainty exist simultaneously, called uncertain random multiobjective programming (URMOP) problem. Since an uncertain random variable does not admit an order relationship, different statistical characteristics can produce different relationship sense between two uncertain random variables. Starting from this idea, several different concepts of Pareto efficient solutions to URMOP problem are provided on the basis of statistical characteristics, such as expected-value efficiency, expected-value variance efficiency, maximum chance efficiency, etc.. Our study enables us to determine what type of efficient solutions should be considered in URMOP problem by each of these concepts. c ©2014 World Academic Press, UK. All rights reserved.