Epistemic foundations of fuzziness : unified theories on decision-choice processes / Kofi Kissi Dompere.

Format:

Book

Author/Creator:

Dompere, K. K.

Series:

Studies in fuzziness and soft computing ; 236.

Studies in fuzziness and soft computing ; 236

Language:

English

Subjects (All):

Uncertainty (Information theory).

Soft computing.

Fuzzy logic.

Physical Description:

xxii, 263 pages : illustrations ; 24 cm.

Place of Publication:

Berlin ; London : Springer, 2009.

Summary:

The series "Studies in Fuzziness and Soft Computing" contains publications on various areas within the so-called soft computing which include fuzzy sets, rough sets, neural networks, evolutionary computations, probabilistic and evidential reasoning, multi-valued logic, and related fields. The publications within "Studies in Fuzziness and Soft Computing" are primarily monographs and edited volumes. They cover significant recent developments in the field, both of a foundational and applicable character. An important feature of the series is its short publication time and world-wide distribution. This permits a rapid and broad dissemination of research results.

Contents:

1 Epistemic Foundations of Fuzzy Mathematics for Decision-Choice Rationality 1

1.1 Reflections on the Role of Mathematics in Knowledge Construct 1

1.2 Uncertainty, Risk and Mathematics 11

1.3 Fuzzification, Defuzzification and Fuzzy Logic 18

1.3.1 Fuzzification in General Fuzzy and Approximate Reasoning 18

2 The Rationality and Two Number Systems 25

2.1 Classical Real Number System and Fuzzy Number System 26

2.1.1 Fuzzification of Classical Real Numbers 27

2.1.2 Defuzzification of Fuzzy Numbers 29

2.2 Defuzzification Methods, Fuzzy Logic and Decision-Rationality in Mathematical Constructs 30

2.3 Examples of Fuzification of Mathematical Strectures for Fuzzy Mathematics and Decision-Choice Rationality 36

2.4 Cohort IV: Fuzzy-Stochastic and Stochastic Fuzzy Spaces 38

2.4.1 The Nature of Fuzzy-Stochastic Space: 41

2.4.2 Rationality, Mathematics and Uncertainties 43

2.5 Some Remarks 47

3 Rationality and Decision-Choice-Theoretic Process 49

3.1 Epistemic Scope of Decision-Choice Rationality 50

3.2 A Canonical Representation of Decision-Choice Theories 52

3.3 A Reflection on Optimality and Rationality 56

3.4 Categories of Information Environment for Decision-Rationality 60

3.5 Information, Knowledge and Uncertainty 65

3.5.1 Past, Present, Future and Decision-Choice Activities 66

4 Non-fuzzy Rationality and the Classical Decision-Choice Process 69

4.1 Complete and Non-fuzzy Information-Knowledge Structure: The Exact Classical Non-stochastic Rationality 70

4.2 Incomplete and Non-fuzzy Information Structure: Exact Classical Stochastic Rationality 74

4.3 The Epistemic Structure of the Classical Rationality 80

4.3.1 Interpretations and Implications of Classical Rationality 82

4.4 From Non-fuzzy Information Structure to Fuzzy Information Structure 84

5 Fuzzy Rationality and Non-classical Decision Processes 91

5.1 Complete and Fuzzy Information Structure and Decision Processes 93

5.2 Decision-Choice Processes with Incomplete and Fuzzy Information Types 99

5.2.1 Separability of Uncertainty Space into Fuzziness and Stochasticity 102

5.3 Non-separability of Uncertainty Space 107

5.3.1 Prior Stochastic Uncertainty to Posterior Fuzzy Uncertainty (Fuzzy Stochastic Rationality) 108

5.3.2 Prior Fuzzy Uncertainty to Posterior Stochastic Uncertainty (Fuzzy Stochastic Rationality) 114

5.4 Some Computational Reflections on Fuzzy-Stochastic Spaces and Decision-Choice Rationality 117

5.4.1 Separability of Fuzzy Uncertainties and Stochastic Uncertainties 118

5.4.2 Non-separability of Fuzzy Uncertainties and Stochastic Uncertainties 119

6 Contraditions, Paradoxes and Fuzzy Optimal Decision-Choice Rationality 121

6.1 Fuzzy Rationality and Contradictions in the Classical Paradigm for Knowledge Construction and Reduction 122

6.2 Fuzzy Decision-Choice Rationality and Paradoxes in Classical Paradigm 129

6.2.1 Fuzzy Decision-Choice Rationality and the Sorites Paradox 131

6.2.2 Indeterminist and Epistemicist Concepts of Vagueness 132

6.3 Problems of Sorites Paradox, Penumbral Regions and Fuzzy Decision-Choice Rationality 134

6.4 Solution to Sorites Paradox by the Method of Optimal Fuzzy Rationality 136

6.4.1 The Sorites Paradox Resolution: The Individual Case by Fuzzy Restriction 141

6.4.2 The Sorites Paradox Resolution: The Collective Case by Fuzzy Restriction 143.

Notes:

Includes bibliographical references and index.

ISBN:

9783540880844

3540880844

OCLC:

269435343