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Axiomatic Fuzzy Set Theory and Its Applications

  • Book
  • © 2009

Overview

Authors:
  1. Xiaodong Liu

    1. Research Center of Information and Control, Dalian University of Technology, Dalian, China

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    You can also search for this author in PubMed   Google Scholar

  2. Witold Pedrycz

    1. Dept. Electrical & Computer Engineering, University of Alberta, Edmonton, Canada

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • First comprehensive, authoritative and up-to-date publication on Axiomatic Fuzzy Set theory
  • Covers detailed mathematical proofs and algorithms

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

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Table of contents (10 chapters)

  1. Front Matter

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  2. Required Preliminary Mathematical Knowledge

    1. Front Matter

      Pages 1-1
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    2. Fundamentals

      • Xiaodong Liu, Witold Pedrycz
      Pages 3-60

    3. Lattices

      • Xiaodong Liu, Witold Pedrycz
      Pages 61-94

  3. Methodology and Mathematical Framework of AFS Theory

    1. Front Matter

      Pages 95-95
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    2. Boolean Matrices and Binary Relations

      • Xiaodong Liu, Witold Pedrycz
      Pages 97-110

    3. AFS Logic, AFS Structure and Coherence Membership Functions

      • Xiaodong Liu, Witold Pedrycz
      Pages 111-166

    4. AFS Algebras and Their Representations of Membership Degrees

      • Xiaodong Liu, Witold Pedrycz
      Pages 167-224

  4. Applications of AFS Theory

    1. Front Matter

      Pages 225-225
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    2. AFS Fuzzy Rough Sets

      • Xiaodong Liu, Witold Pedrycz
      Pages 227-267

    3. AFS Topology and Its Applications

      • Xiaodong Liu, Witold Pedrycz
      Pages 269-301

    4. AFS Formal Concept and AFS Fuzzy Formal Concept Analysis

      • Xiaodong Liu, Witold Pedrycz
      Pages 303-349

    5. AFS Fuzzy Clustering Analysis

      • Xiaodong Liu, Witold Pedrycz
      Pages 351-421

    6. AFS Fuzzy Classifiers

      • Xiaodong Liu, Witold Pedrycz
      Pages 423-489

  5. Back Matter

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Keywords

About this book

It is well known that “fuzziness”—informationgranulesand fuzzy sets as one of its formal manifestations— is one of important characteristics of human cognitionandcomprehensionofreality. Fuzzy phenomena existinnature and are encountered quite vividly within human society. The notion of a fuzzy set has been introduced by L. A. , Zadeh in 1965 in order to formalize human concepts, in connection with the representation of human natural language and computing with words. Fuzzy sets and fuzzy logic are used for mod- ing imprecise modes of reasoning that play a pivotal role in the remarkable human abilities to make rational decisions in an environment a?ected by - certainty and imprecision. A growing number of applications of fuzzy sets originated from the “empirical-semantic” approach. From this perspective, we were focused on some practical interpretations of fuzzy sets rather than being oriented towards investigations of the underlying mathematical str- tures of fuzzy sets themselves. For instance, in the context of control theory where fuzzy sets have played an interesting and practically relevant function, the practical facet of fuzzy sets has been stressed quite signi?cantly. However, fuzzy sets can be sought as an abstract concept with all formal underpinnings stemming from this more formal perspective. In the context of applications, it is worth underlying that membership functions do not convey the same meaning at the operational level when being cast in various contexts.

Authors and Affiliations

  • Research Center of Information and Control, Dalian University of Technology, Dalian, China

    Xiaodong Liu

  • Dept. Electrical & Computer Engineering, University of Alberta, Edmonton, Canada

    Witold Pedrycz

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