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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 657978, 9 pages
http://dx.doi.org/10.1155/2013/657978
Research Article

Fuzzy Group Decision Making for Multiobjective Problems: Tradeoff between Consensus and Robustness

1Department of Management, College of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, China
2School of Software, Shenzhen Institute of Information Technology, Shenzhen 518172, China

Received 3 April 2013; Revised 24 June 2013; Accepted 12 July 2013

Academic Editor: Jianming Zhan

Copyright © 2013 Jian Xiong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Many decision making problems involve multiple decision makers and conflicting objectives. This paper refers to this kind of problems as group decision making for multiobjective problems (GDM-MOP). The task of GDM-MOP is to select final solution(s) from a set of nondominated solutions according to the decision makers' preferences. However, it is common that the preference could be imprecise. We study the GDM-MOP where preferences are expressed by fuzzy reference points, called as fuzzy GDMMOP (FGDM-MOP). This paper provides a decision support model to simultaneously consider two measures for FGDM-MOP: consensus measure and robustness measure. The former is used to reflect the acceptable degree of a solution by the decision making group, while the latter indicates a solution's ability to cope with any change on preferences. A multiobjective evolutionary approach is presented to solve the problem. Finally, a modified benchmark function is studied to illustrate the proposed approach.