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Mathematical Problems in Engineering
Volume 2015, Article ID 826752, 11 pages
Research Article

Extended Duality in Fuzzy Optimization Problems

Information Science and Technology College, Dalian Maritime University, Dalian 116026, China

Received 6 January 2014; Revised 15 October 2014; Accepted 19 October 2014

Academic Editor: Tsung-Chih Lin

Copyright © 2015 Tingting Zou. 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.


Duality theorem is an attractive approach for solving fuzzy optimization problems. However, the duality gap is generally nonzero for nonconvex problems. So far, most of the studies focus on continuous variables in fuzzy optimization problems. And, in real problems and models, fuzzy optimization problems also involve discrete and mixed variables. To address the above problems, we improve the extended duality theory by adding fuzzy objective functions. In this paper, we first define continuous fuzzy nonlinear programming problems, discrete fuzzy nonlinear programming problems, and mixed fuzzy nonlinear programming problems and then provide the extended dual problems, respectively. Finally we prove the weak and strong extended duality theorems, and the results show no duality gap between the original problem and extended dual problem.