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Complexity
Volume 2017 (2017), Article ID 9317924, 12 pages
https://doi.org/10.1155/2017/9317924
Research Article

On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach

Department of Applied Mathematics, School of Mathematics and Computer Science, Damghan University, Damghan, Iran

Correspondence should be addressed to Omid Solaymani Fard; moc.liamg@drafsdimo

Received 26 May 2017; Accepted 24 July 2017; Published 14 September 2017

Academic Editor: Carla Pinto

Copyright © 2017 Omid Solaymani Fard and Mohadeseh Ramezanzadeh. 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

Fuzzy portfolio selection problem is a major issue in the financial field and a special case of constrained fuzzy-valued optimization problems (CFOPs). In this respect, the present paper aims to investigate the CFOP with regard to the features of the parametric representation of fuzzy numbers named as convex constraint function (CCF) which is proposed by Chalco-Cano et al. in 2014. Furthermore, relying on this parametric representation, some proper conditions are provided for the existence of solutions to a CFOP. To this end, by the increasing representation of CCF, the main problem is converted to a parametric multiobjective programming problem and some solution concepts from a similar framework in the multiobjective programming are proposed for the CFOP. Eventually to illustrate the proposed results, the fuzzy portfolio selection problem is discussed.