An ontological and epistemological perspective of fuzzy set theory / I. Burhan Turksen.

Format:

Book

Author/Creator:

Turksen, I. Burhan, 1937-

Language:

English

Subjects (All):

Fuzzy sets.

Set theory.

Physical Description:

1 online resource (543 p.)

Edition:

1st ed.

Place of Publication:

Amsterdam ; Oxford : Elsevier, 2006.

Language Note:

English

System Details:

text file

Summary:

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 uppe

Contents:

Front Cover; AN ONTOLOGICAL AND EPISTEMOLOGICAL PERSPECTIVE OF FUZZY SET THEORY; Copyright Page; FOREWORD; PREFACE; CONTENTS; Chapter 0. FOUNDATION; 0.1. A Personal Perspective; 0.2. A Perspective on The Philosophical Grounding of Fuzzy Theories; Chapter 1. INTRODUCTION; 1.1. Description and Verity; 1.2. Nature of Truth; 1.3. Definiteness vs. Indefiniteness; 1.4. Syntax of a Formal Language, a PNL; 1.5. Basic Notations - Type 1 Theory; 1.6. Basic Notations - Type 2 Theory; 1.7. Epistemological Concerns; Chapter 2. COMPUTING WITH WORDS; 2.1. Words to Numbers

2.2. Descriptive and Veristic Assignments2.3. Structure of Sentences; Chapter 3. MEASUREMENT OF MEMBERSHIP; 3.1. Interpretations of Grade of Membership; 3.2. Measurement Theory View; 3.3. Membership and Connectives; Chapter 4. ELICITATION METHODS; 4.1. Polling Methods; 4.2. Direct Rating Methods; 4.3. Reverse Rating; 4.4. Interval Estimation; 4.5. Membership Exemplification; 4.6. Pair wise Comparison; 4.7. General Remarks on Subjective Methods; Chapter 5. FUZZY CLUSTERING METHOD; 5.1. Fuzzy Clustering Techniques; 5.2. Type 2 Fuzziness; 5.3. Curve Fitting to Membership Values

5.4. Newal-fuzzy TechniqueChapter 6. CLASSES OF FUZZY SET AND LOGIC THEORIES; 6.1. Linguistic Expression; 6.2. Meta-Linguistic Expression; 6.3. Propositional Expression; 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; Chapter 7. EQUIVALENCES IN TWO-VALUED LOGIC; 7.1. Two-Valued Set(Description) and Two-Valued Logic(Verification); 7.2. (Canonical) Normal Form Derivation

7.3. Equivalence of Normal Forms7.4. Direct Fuzzification of DNF and CNF Expression; 7.5. Consequences of D{0,1} V{0,1}; 7.6. Symbols, Proposition and Predicates; Chapter 8. FUZZY-VALUED SET AND TWO-VALUED LOGIC; 8.1. New Construction of 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; 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 Triples9.5. 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; Chapter 10. CONSEQUENCES OF {D[0,1], V{0,1}}} THEORY; 10.1. Laws of Middle and Contradiction; 10.2. Zadehean Fuzzy Middle and Contradiction; 10.3. Fuzzy Middle and Fuzzy Contradiction with t-norms and co-norms; 10.4. Laws of Fuzzy Conservation; 10.5. Canonical Forms of Re-Affirmation And Re-Negation; 10.6. Canonical Forms of Re-Negation; 10.7. Conclusion; Chapter 11. COMPENSATORY ""AND""

11.1. Exponential-Compensatory ""AND""

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611025434

9781281025432

1281025437

9780080525716

0080525717

OCLC:

437182087