Basic Concepts of Fuzzy Logic

  • Freerk A. Lootsma
Part of the Applied Optimization book series (APOP, volume 8)


This chapter starts from the mathematical model of vagueness and imprecision originally proposed by Zadeh (1965) who suspected that an ever-increasing amount of precision in mathematical modelling would lead to almost insignificant models for control systems. Fuzzy-set theory experienced considerable resistance from probability theory, but in electrical engineering it is now widely accepted as a suitable model for the verbal classification of observations and control commands.


Membership Function Fuzzy Logic Fuzzy Number Arithmetic Operation Triangular Fuzzy Number 
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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References to Chapter 2

  1. 1.
    Bellman, R., and Giertz, M., “On the Analytic Formalism of the Theory of Fuzzy Sets”. Information Science 5, 149 – 156, 1973.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Dubois, D., and Prade, H., “Fuzzy Sets and Systems, Theory and Applications”. Academic Press, New York, 1980.zbMATHGoogle Scholar
  3. 3.
    Kosko, B., “Neural Networks and Fuzzy Systems”. Prentice Hall, Englewood Cliffs, New Jersey, 1992.zbMATHGoogle Scholar
  4. 4.
    Rosch, E., “Principles of Categorization”. In E. Rosch and B. Lloyds (eds.), “Cognition and Categorization”. Lawrence Erlbaum, Hillsdale, New Jersey, 1978, pp. 27 – 48.Google Scholar
  5. 5.
    Zadeh, LA., “Fuzzy Sets”. Information and Control 8, 338 – 353, 1965.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1997

Authors and Affiliations

  • Freerk A. Lootsma
    • 1
  1. 1.Delft University of TechnologyThe Netherlands

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