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Evaluating Linguistic Expressions and Functional Fuzzy Theories in Fuzzy Logic

  • Vilém Novák
  • Irina Perfilieva
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 33)

Abstract

In this paper, we introduce a new mathematical model of the meaning of the basic linguistic trichotomy, which are the canonical words “small”, “medium” and “big”. The model is based on the concept of horizon as elaborated in the Alternative Set Theory. Such a model makes also possible to include naturally the linguistic hedges which form a consistent class of functions. Each linguistic hedge is thus characterized by one number only.

Then it is shown that continuous functional dependences between x and y can be described (precisely or approximately) by the collections of logical formulas of implicative form with predicates interpreted by fuzzy sets with meaning of the basic linguistic trichotomy. It demonstrates the expressive power of modified by linguistic hedges membership functions of fuzzy sets from the basic triplet.

Keywords

Membership Function Fuzzy Logic Fuzzy Number Linguistic Term Fuzzy Logic Controller 
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-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Vilém Novák
    • 1
    • 2
  • Irina Perfilieva
    • 3
  1. 1.Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstrava 1Czech Republic
  2. 2.Institute of the Theory of Information and AutomationAcademy of Sciences of the Czech RepublicPraha 8Czech Republic
  3. 3.Moscow State Academy of Instrument MakingMoscowRussia

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