Axiomatic Fuzzy Set Theory and Its Applications

  • Xiaodong Liu
  • Witold Pedrycz

Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 244)

Table of contents

  1. Front Matter
  2. Required Preliminary Mathematical Knowledge

    1. Front Matter
      Pages 1-1
    2. Xiaodong Liu, Witold Pedrycz
      Pages 3-60
    3. Xiaodong Liu, Witold Pedrycz
      Pages 61-94
  3. Methodology and Mathematical Framework of AFS Theory

    1. Front Matter
      Pages 95-95
    2. Xiaodong Liu, Witold Pedrycz
      Pages 97-110
    3. Xiaodong Liu, Witold Pedrycz
      Pages 111-166
    4. Xiaodong Liu, Witold Pedrycz
      Pages 167-224
  4. Applications of AFS Theory

    1. Front Matter
      Pages 225-225
    2. Xiaodong Liu, Witold Pedrycz
      Pages 227-267
    3. Xiaodong Liu, Witold Pedrycz
      Pages 269-301
    4. Xiaodong Liu, Witold Pedrycz
      Pages 303-349
    5. Xiaodong Liu, Witold Pedrycz
      Pages 351-421
    6. Xiaodong Liu, Witold Pedrycz
      Pages 423-489
  5. Back Matter

About this book

Introduction

In the age of Machine Intelligence and computerized decision making, we have to deal with subjective imprecision inherently associated with human perception and described in natural language and uncertainty captured in the form of randomness. This treatise develops the fundamentals and methodology of Axiomatic Fuzzy Sets (AFS), in which fuzzy sets and probability are treated in a unified and coherent fashion. It offers an efficient framework that bridges real world problems with abstract constructs of mathematics and human interpretation capabilities cast in the setting of fuzzy sets.

In the self-contained volume, the reader is exposed to the AFS being treated not only as a rigorous mathematical theory but also as a flexible development methodology for the development of intelligent systems.

The way in which the theory is exposed helps reveal and stress linkages between the fundamentals and well-delineated and sound design practices of practical relevance. The algorithms being presented in a detailed manner are carefully illustrated through numeric examples available in the realm of design and analysis of information systems.

The material can be found equally advantageous to the readers involved in the theory and practice of fuzzy sets as well as those interested in mathematics, rough sets, granular computing, formal concept analysis, and the use of probabilistic methods.

Keywords

AFS Theory Applications of AFS Theory Axiomatic Fuzzy Set Theory Fuzziness Mathematica algebra fuzzy intelligent systems knowledge

Authors and affiliations

  • Xiaodong Liu
    • 1
  • Witold Pedrycz
    • 2
  1. 1.Research Center of Information and ControlDalian University of TechnologyDalianChina
  2. 2.Dept. Electrical & Computer EngineeringUniversity of AlbertaEdmontonCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-00402-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-00401-8
  • Online ISBN 978-3-642-00402-5
  • Series Print ISSN 1434-9922
  • Series Online ISSN 1860-0808
  • About this book