Fuzzy Mathematical Programming

  • Jaroslav Ramík
  • Milan Vlach
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 41)


Mathematical programming problems (MP) can be considered as decision making problems in which preferences between alternatives are described by means of objective functions on a given set of alternatives in such a way that more preferable alternatives have higher values. The values of the objective function describe effects from choices of the alternatives. In economic problems, for example, these values may reflect profits obtained when using various means of production. The set of feasible alternatives in MP problems is described implicitly by means of constraints — equations or inequalities, or both — representing relevant relationships between alternatives. In any case the results of the analysis using given formulation of the MP problem depend largely upon how adequately various factors of the real system are reflected in the description of the objective function(s) and of the constraints.


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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Jaroslav Ramík
    • 1
  • Milan Vlach
    • 2
    • 3
  1. 1.School of Business AdministrationSilesian UniversityKarvináCzech Republic
  2. 2.School of Information ScienceJapan Advanced Institute of Science and TechnologyIshikawaJapan
  3. 3.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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