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Fuzzy Optimization and Mathematical Programming: A Brief Introduction and Survey

  • Chapter
Optimization Models Using Fuzzy Sets and Possibility Theory

Part of the book series: Theory and Decision Library ((TDLB,volume 4))

Abstract

Some general concepts and ideas related to fuzzy optimization as, e.g., a fuzzy constraint, fuzzy goal (objective function), fuzzy optimum, etc. are introduced first. A general fuzzy optimization problem involving these elements is formulated and solved. The cases of single and multiple objective functions are dealt with. Secondly, basic classes of fuzzy mathematical programming are discussed, including: fuzzy linear programming (with single and multiple objective functions), fuzzy integer programming, fuzzy 0–1 programming and fuzzy dynamic programming. Finally some newer, knowledge-based approaches are mentioned. An extended list of literature is included.

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Authors and Affiliations

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

    Janusz Kacprzyk

  2. International Institute for Applied Systems Analysis (IIASA), A-2361, Laxenburg, Austria

    Sergei A. Orlovski

  3. Computing Center of the USSR, Academy of Sciences, Moscow, USSR

    Sergei A. Orlovski

Authors
  1. Janusz Kacprzyk
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  2. Sergei A. Orlovski
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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    J. Kacprzyk

  2. International Institute for Applied Systems Analysis, Laxenburg, Austria

    S. A. Orlovski

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Kacprzyk, J., Orlovski, S.A. (1987). Fuzzy Optimization and Mathematical Programming: A Brief Introduction and Survey. In: Kacprzyk, J., Orlovski, S.A. (eds) Optimization Models Using Fuzzy Sets and Possibility Theory. Theory and Decision Library, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3869-4_4

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