An Ontological and Epistemological Perspective of Fuzzy Set Theory

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

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