Fuzzy costs in quadratic programming problems
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Although quadratic programming problems are a special class of nonlinear programming, they can also be seen as general linear programming problems. These quadratic problems are of the utmost importance in an increasing variety of practical fields. As, in addition, ambiguity and vagueness are natural and ever-present in real-life situations requiring operative solutions, it makes perfect sense to address them using fuzzy concepts formulated as quadratic programming problems with uncertainty, i.e., as Fuzzy Quadratic Programming problems. This work proposes two novel fuzzy-sets-based methods to solve a particular class of Fuzzy Quadratic Programming problems which have vagueness coefficients in the objective function. Moreover, two other linear approaches are extended to solve the quadratic case. Finally, it is shown that the solutions reached from the extended approaches may be obtained from two proposed parametric multiobjective approaches.
KeywordsFuzzy set Decision making Fuzzy mathematical optimization Quadratic programming Efficient solutions
The authors want to thank the financial support from the agency FAPESP (project number 2010/51069-2) and the Spanish projects CEI BioTic GENIL from the MICINN, as well as TIN2011-27696-C02-01, P11-TIC-8001, TIN2008-06872-C04-04, and TIN2008-01948.
- Bector, C. R., & Chandra, S. (2005). Fuzzy mathematical programming and fuzzy matrix games, volume 169 of studies in fuzziness and soft computing. Berlin: Springer.Google Scholar
- Hock, W., & Schittkowski, K. (1981). Test examples for nonlinear programming codes, volume 187 of lecture notes in economics and mathematical systems. Berlin: Spring.Google Scholar
- Ida, M. (2003). Portfolio selection problem with interval coefficients. Applied Mathematics Letters, 16, 709–713.Google Scholar
- Lai, Y. J., & Hwang, C. L. (1992). Fuzzy mathematical programming: Methods and applications, volume 394 of lecture notes in economics and mathematical systems. Berlin: Springer.Google Scholar
- Schittkowski, K. (1987). More test examples for nonlinear programming codes, volume 282 of lecture notes in economics and mathematical systems. Berlin: Springer.Google Scholar
- Silva, R. C., Cruz, C., Verdegay, J. L., & Yamakami, A. (2010a). A survey of fuzzy convex programming models. In L. Weldon & J. Kacprzyk (Eds.), Fuzzy optimization: Recent advances and applications, volume 254 of studies in fuzziness and soft computing. Berlin: Springer.Google Scholar
- Silva, R. C., Verdegay, J. L., & Yamakami, A. (2010b). A parametric convex programming approach applied in portfolio selection problem with fuzzy costs. In 2010 IEEE international fuzzy systems conference, Barcelona, FUZZ-IEEE 2010.Google Scholar