Fuzzy Optimization and Decision Making

, Volume 12, Issue 3, pp 231–248 | Cite as

Fuzzy costs in quadratic programming problems

  • Ricardo C. Silva
  • Carlos Cruz
  • José L. Verdegay


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.


Fuzzy 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.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Ricardo C. Silva
    • 1
  • Carlos Cruz
    • 2
  • José L. Verdegay
    • 2
  1. 1.Institute of Science and TechnologyFederal University of São PauloSão José dos CamposBrazil
  2. 2.Department of Computer Science and Artificial IntelligenceCITIC–University of GranadaGranadaSpain

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