Fuzzy Sets and Their Operations

  • Evangelos Triantaphyllou
Part of the Applied Optimization book series (APOP, volume 44)


For a long time it has been recognized that an exact description of many real life physical situations may be virtually impossible. This is due to the high degree of imprecision involved in real world situations. Zadeh, in his seminal papers [Zadeh, 1965; and 1968], proposed fuzzy set theory as the means for quantifying the inherent fuzziness that is present in ill-posed problems (which by many accounts are the majority of the real life problems in decision making). Fuzziness is a type of imprecision which may be associated with sets in which there is no sharp transition from membership to nonmembership [Bellman and Zadeh, 1970]. Examples of fuzzy sets are classes of objects (entities) characterized by such adjectives as large, small, serious, simple, approximate, etc. [Bellman and Zadeh, 1970].


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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Evangelos Triantaphyllou
    • 1
  1. 1.Department of Industrial and Manufacturing Systems Engineering, College of EngineeringLouisiana State UniversityBaton RougeUSA

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