Probability Applications

Contents
Foreword
Lotfi A. Zadeh
Foreword
Patrick Suppes
Preface
Acknowledgments
xv
xix
xxi
xxiii
Part I. Fundamentals 1
Jane M. Booker
1.1 Chapters 1-6 1
1.2 Suggested reading 2
References 2
1 Introduction 3
Timothy J. Ross, Jane M. Booker, and W. Jerry Parkinson
1.1 Some history and initial thoughts 3
1.2 The great debate 6
1.2.1 The debate literature 6
1.2.2 The issues and controversy 7
1.3 Fuzzy logic and probability: The best of both worlds 20
1.4 Organization of the book 22
References 24
2 Fuzzy Set Theory, Fuzzy Logic, and Fuzzy Systems 29
Timothy J. Ross and W. Jerry Parkinson
2.1 Introduction 29
2.1.1 Fuzzy sets 31
2.1.2 Fuzzy set operations 32
2.2 Fuzzy relations 34
2.2.1 Operations on fuzzy relations 34
2.2.2 Fuzzy Cartesian product and composition 35
2.3 Fuzzy and classical logic 36
2.3.1 Classical logic 36
2.3.2 Fuzzy logic 41
2.3.3 Approximate reasoning 43
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