Fuzzy Multi-Criteria Decision Making

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


When dealing with practical decision problems, we often have to take into consideration uncertainty in the problem data. It may arise from errors in measuring physical quantities, from errors caused by representing some data in a computer, from the fact that some data are approximate solutions of other problems or estimations by human experts, etc. In some of these situations, the fuzzy set approach may be applicable. In the context of multicriteria decision making, functions mapping the set of feasible alternatives into the unit interval [0, 1] of real numbers representing normalized utility functions can be interpreted as membership functions of fuzzy subsets of the underlying set of alternatives. However, functions with the range in [0, 1] arise in more contexts.


Membership Function Fuzzy Subset Aggregation Operator Generalize Concavity Fuzzy Criterion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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