An Ontological and Epistemological Perspective of Fuzzy Set Theory

1st Edition

Authors: I. Burhan Türksen
Hardcover ISBN: 9780444518910
eBook ISBN: 9780080525716
Imprint: Elsevier Science
Published Date: 15th November 2005
Page Count: 542
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Description

Fuzzy set and logic theory suggest that all natural language linguistic expressions are imprecise and must be assessed as a matter of degree. But in general membership degree is an imprecise notion which requires that Type 2 membership degrees be considered in most applications related to human decision making schemas. Even if the membership functions are restricted to be Type1, their combinations generate an interval – valued Type 2 membership. This is part of the general result that Classical equivalences breakdown in Fuzzy theory. Thus all classical formulas must be reassessed with an upper and lower expression that are generated by the breakdown of classical formulas.

Key features:

  • Ontological grounding
  • Epistemological justification
  • Measurement of Membership
  • Breakdown of equivalences
  • FDCF is not equivalent to FCCF
  • Fuzzy Beliefs
  • Meta-Linguistic axioms

Key Features

  • Ontological grounding
  • Epistemological justification
  • Measurement of Membership
  • Breakdown of equivalences
  • FDCF is not equivalent to FCCF
  • Fuzzy Beliefs
  • Meta-Linguistic axioms

Readership

Fuzzy set and Logic theory and applications, Industrial Engineering, Management Sciences, Operations Research, Decision Support Systems and System Modeling.

Table of Contents

Table of Contents

Preface Table of Contents

  1. Foundation
  2. Introduction
  3. Computing with Words
  4. Measurement of Membership
  5. Elicitation Methods
  6. Fuzzy Clustering Methods
  7. Classes of Fuzzy Set and Logic Theories
  8. Equivalences in Two-Valued Logic
  9. Fuzzy-Valued Set and Two-Valued Logic
  10. Containment of FDCF in FCCF
  11. Consequences of D(0,1), V(0,1) Theory
  12. Compensatory "And"
  13. Belief, Plausibility and Probability Measures on Interval-Valued Type 2 Fuzzy Sets
  14. Veristic Fuzzy Sets of Truthoods
  15. Approximate Reasoning
  16. Interval-Valued Type 2 GMP
  17. A Theoretical Application of Interval-Valued Type 2 Representation
  18. A Foundation for Computing with Words: Meta-Linguistic Axioms
  19. Epilogue References Subject Index Author Index

Details

No. of pages:
542
Language:
English
Copyright:
© Elsevier Science 2006
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080525716
Hardcover ISBN:
9780444518910

About the Author

I. Burhan Türksen