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Journal of Applied Mathematics
Volume 2014, Article ID 489893, 8 pages
Research Article

Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients

1School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China
2Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, China
3Department of Mathematical Sciences, University of Mazandaran, P.O. Box 47415-1468, Babolsar, Iran

Received 16 January 2014; Accepted 27 March 2014; Published 23 April 2014

Academic Editor: Mohammad Khodabakhshi

Copyright © 2014 Xue-Gang Zhou 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.


The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP) in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.