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Mathematical Principles of Fuzzy Logic

  • Book
  • © 1999

Overview

Authors:
  1. Vilém Novák

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

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  2. Irina Perfilieva

    1. Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava 1, Czech Republic
      Moscow State Academy of Instrument Making, Moscow, Russia

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  3. Jiří Močkoř

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

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Part of the book series: The Springer International Series in Engineering and Computer Science (SECS, volume 517)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Fuzzy Logic: What, Why, for Which?

    • Vilém Novák, Irina Perfilieva, Jiří Močkoř
    Pages 1-14

  3. Algebraic Structures for Logical Calculi

    • Vilém Novák, Irina Perfilieva, Jiří Močkoř
    Pages 15-60

  4. Logical Calculi and Model Theory

    • Vilém Novák, Irina Perfilieva, Jiří Močkoř
    Pages 61-93

  5. Fuzzy Logic in Narrow Sense

    • Vilém Novák, Irina Perfilieva, JiŘí Močkoř
    Pages 95-178

  6. Functional Systems in Fuzzy Logic Theories

    • Vilém Novák, Irina Perfilieva, JiŘí Močkoř
    Pages 179-222

  7. Fuzzy Logic in Broader Sense

    • Vilém Novák, Irina Perfilieva, JiŘí Močkoř
    Pages 223-257

  8. Topoi and Categories of Fuzzy Sets

    • Vilém Novák, Irina Perfilieva, JiŘí Močkoř
    Pages 259-297

  9. Few Historical and Concluding Remarks

    • Vilém Novák, Irina Perfilieva, JiŘí Močkoř
    Pages 299-303

  10. Back Matter

    Pages 305-320
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Keywords

About this book

Mathematical Principles of Fuzzy Logic provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what can be represented, and how, by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter.
This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of commonsense human reasoning, based on the use of natural language, the distinguishing feature of which is the vagueness of its semantics.

Authors and Affiliations

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

    Vilém Novák, Irina Perfilieva, Jiří Močkoř

  • Moscow State Academy of Instrument Making, Moscow, Russia

    Irina Perfilieva

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