Book 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
- Ontological grounding- Epistemological justification- Measurement of Membership- Breakdown of equivalences- FDCF is not equivalent to FCCF- Fuzzy Beliefs- Meta-Linguistic axioms
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- FOREWORD
- PREFACE
- Chapter 0: FOUNDATION
- Chapter 1: INTRODUCTION
- Chapter 2: COMPUTING WITH WORDS
- Chapter 3: MEASUREMENT OF MEMBERSHIP
- Chapter 4: ELICITATION METHODS
- Chapter 5: FUZZY CLUSTERING METHOD
-
Chapter 6: CLASSES OF FUZZY SET AND LOGIC THEORIES
- 6.1 Linguistic Expression
- 6.2 Meta-Linguistic Expression
- 6.3 Propositional Expressions
- 6.4 Classes of Fuzzy Sets and Two-Valued Logic
- 6.5 Sub-Sub Classes of t-Norms
- 6.6 Sub-Sub Classes of t-Conorms
- 6.7 Fuzzy-Set Complements
- 6.8 De Morgan Triples
- 6.9 Parametric t-norms and t-conorms
- 6.10 Fundamental Phrases and Clauses
- Appendix 6.1 Basic Properties of negations and t-norms
- Chapter 7: EQUIVALENCES IN TWO-VALUED LOGIC
-
Chapter 8: FUZZY-VALUED SET AND TWO-VALUED LOGIC
- 8.1 New Construction of the Truth Tables
- 8.2 Dempster-Pawlak Unification
- 8.3 DEMPSTER and PAWLAK Formulations
- 8.4 Sets and Logic Constructs
- 8.5 Generalization
- 8.6 Interval-Valued Type 2 Fuzzy Empty and Universal Sets
- Appendix 8.1 Fuzzy Canonical Form Derivation Algorithm
- Appendix 8.2 Canonical Form Derivation with Set Membership Consideration
-
Chapter 9: CONTAINMENT OF FDCF IN FCCF
- 9.1 Generators of Continuous Archimedean Norms
- 9.2 Non Archimedean Triangular Norms and Conorms
- 9.3 Ordinal Sums
- 9.4 De Morgan Triples
- 9.5 Basic Protoforms: FDCF and FCCF
- 9.6 Preliminary Observations
- 9.7 Containment for continuous Archimedean t-norms
- 9.8 Combination of More Than Two Propositions
- Appendix 9.1 (Bilgic, 1995)
- Appendix 9.2 (Bilgic, 1995)
- Chapter 10: CONSEQUENCES OF {D[0,1], V{0,1}}} THEORY
- Chapter 11: COMPENSATORY “AND”
- Chapter 12: BELIEF, PLAUSIBILITY AND PROBABILITY MEASURES ON INTERVAL-VALUED TYPE 2 FUZZY SETS
- Chapter 13: VERISTIC FUZZY SETS OF TRUTHOODS
-
Chapter 14: APPROXIMATE REASONING
- 14.1 Classical Reasoning Methods
- 14.2 Classical Modus Ponens
- 14.3 Generalized Modus Ponens
- 14.4 Type 1 Fuzzy Rules
- 14.5 Type 1 Fuzzy Inference: Single Antecedent GMP
- 14.6 Information Gap in Type 1 GMP
- 14.7 Type 1 Fuzzy Inference: Two Antecedent GMP
- 14.8 Decomposition
- 14.9 Computational Complexity
- 14.10 Implementation with Type 1 Reasoning
- 14.11 Type 1 Fuzzy System Modeling
- 14.12 Case studies
- Appendix 14.1 Brief explanation of the proposed stages of fuzzy system modeling
-
Chapter 15: INTERVAL-VALUED TYPE 2 GMP
- 15.1 Interval-Valued Type 2 Fuzzy Rules
- 15.2 Some Properties Interval-Valued Type 2 Implication
- 15.3 Information Gap in Interval-Valued Type 2 GMP
- 15.4 Implementations of Interval-Valued Type 2 Reasoning
- 15.5 Interval-Valued Type 2 System Modeling
- 15.6 Application to Case Studies with Interval Valued Type 2 Reasoning
- 15.6.2 Conclusion
- Appendix 15.1
- Appendix 15.1 Representation of rules
- Appendix 15.3 Actual output data vs the results of reasoning methods
- Chapter 16: A THEORETICAL APPLICATION OF INTERVAL-VALUED TYPE 2 REPRESENTATION
- Chapter 17: A FOUNDATION FOR COMPUTING WITH WORDS: META-LINGUISTIC AXIOMS
- EPILOGUE
- REFERENCES
- INDEX
- AUTHOR INDEX
Product information
- Title: An Ontological and Epistemological Perspective of Fuzzy Set Theory
- Author(s):
- Release date: November 2005
- Publisher(s): Elsevier Science
- ISBN: 9780080525716
You might also like
book
Fuzzy Set and Its Extension
Provides detailed mathematical exposition of the fundamentals of fuzzy set theory, including intuitionistic fuzzy sets This …
book
Combinatorics of Set Partitions
Focusing on a very active area of mathematical research in the last decade, this book presents …
book
Designing Scientific Applications on GPUs
Many of today's complex scientific applications now require a vast amount of computational power. General purpose …
book
Photonic Signals and Systems: An Introduction
Build the skills needed to engineer next-generation systems using light Photonic Signals and Systems: An Introduction …