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Fuzzy/Linguistic IF-THEN Rules and Linguistic Descriptions

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Encyclopedia of Database Systems

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Definition

Fuzzy/linguistic IF-THEN rules are structured expressions of natural language having the form

$$ \mathrm{\mathcal{R}}\kern0.5em =\kern0.5em IF\kern0.5em X\kern0.5em is\kern0.5em \mathcal{A}\kern0.5em THEN\kern0.5em Y\kern0.5em is\kern0.5em \mathrm{\mathcal{B}} $$
(1)

where X, Y are variables and \( \mathcal{A},\kern0.5em \mathrm{\mathcal{B}} \) are expressions such as small, very small, medium, roughly medium, more or less big, big, etc. The latter are called evaluative linguistic expressions. Modeling their meaning in fuzzy set theory makes it possible to model the meaning of the whole rule. The part before THEN is called antecedent, the part after it is called consequent.

A linguistic description is a finite set of fuzzy/linguistic IF-THEN rules

$$ \begin{array}{l}{\mathrm{\mathcal{R}}}_1:\kern0.5em \mathrm{IF}\kern0.5em X\kern0.5em \mathrm{is}\kern0.5em {\mathcal{A}}_1\kern0.5em \mathrm{THEN}\kern0.5em Y\kern0.5em \mathrm{is}\kern0.5em {\mathrm{\mathcal{B}}}_1\\...

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Recommended Reading

  1. Klir GJ, Yuan B. Fuzzy sets and fuzzy logic: theory and applications. New York: Prentice-Hall; 1995.

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  2. Novák V, Lehmke S. Logical structure of fuzzy IF-THEN rules. Fuzzy Set Syst. 2006;157(15):2003–29.

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  3. Novák V, Perfilieva I. On the semantics of perception-based fuzzy logic deduction. Int J Intell Syst. 2004;19(11):1007–31.

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  4. Novák V, Perfilieva I, Močkoř J. Mathematical principles of fuzzy logic. Boston/Dordrecht: Kluwer; 1999.

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Author information

Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic

    Vilém Novák

Authors
  1. Vilém Novák
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Correspondence to Vilém Novák .

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology College of Computing, Atlanta, GA, USA

    Ling Liu

  2. University of Waterloo School of Computer Science, Waterloo, ON, Canada

    M. Tamer Özsu

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Novák, V. (2018). Fuzzy/Linguistic IF-THEN Rules and Linguistic Descriptions. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_5011

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