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Fuzzy Optimization pp 127–143Cite as

A Survey of Fuzzy Convex Programming Models

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 254))

Abstract

Optimization is a procedure of finding and comparing feasible solutions until no better solution can be found. It can be divided into several fields, one of which is the Convex Optimization. It is characterized by a convex objective function and convex constraint functions over a convex set which is the set of the decision variables. This can be viewed, on the one hand, as a particular case of nonlinear programming and, on the other hand, as a general case of linear programming. Convex optimization has applications in a wide range of real-world applications, whose data often cannot be formulate precisely. Hence it makes perfect sense to apply fuzzy set theory as a way to mathematically describe this vagueness. In this paper we review the theory about this topic and describe some flexible and possibilistic programming models to solve fuzzy convex programming problems. Flexible programming uses fuzzy sets to represent the vagueness of the decision maker’s aspirations and constraints, while possibilistic programming models imprecise or ambiguous data by possibility distributions.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Artificial Intelligence, University of Granada, E-18071, Granada, Spain

    Carlos Cruz & José L. Verdegay

  2. Department of Telematics, School of Electrical and Computer Engineering, University of Campinas, P.O. Box 6101, 13083-970, Campinas, SP, Brazil

    Ricardo C. Silva & Akebo Yamakami

Authors
  1. Ricardo C. Silva
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  2. Carlos Cruz
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  3. José L. Verdegay
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  4. Akebo Yamakami
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Editor information

Editors and Affiliations

  1. Department of Mathemaitical and Statistical Sciences, University of Colorado Denver, PO Box 173364, 80217-3364, Colorado, Denver, USA

    Weldon A. Lodwick

  2. Systems Research Institute Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

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Silva, R.C., Cruz, C., Verdegay, J.L., Yamakami, A. (2010). A Survey of Fuzzy Convex Programming Models. In: Lodwick, W.A., Kacprzyk, J. (eds) Fuzzy Optimization. Studies in Fuzziness and Soft Computing, vol 254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13935-2_6

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  • DOI: https://doi.org/10.1007/978-3-642-13935-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13934-5

  • Online ISBN: 978-3-642-13935-2

  • eBook Packages: EngineeringEngineering (R0)

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