Fuzzy Measure Theory / Edition 1

Fuzzy Measure Theory / Edition 1

by Zhenyuan Wang, George Klir
     
 

ISBN-10: 0306442604

ISBN-13: 9780306442605

Pub. Date: 01/31/1993

Publisher: Springer US

Providing the first comprehensive treatment of the subject, this groundbreaking work is solidly founded on a decade of concentrated research, some of which is published here for the first time, as well as practical, ''hands on'' classroom experience. The clarity of presentation and abundance of examples and exercises make it suitable as a graduate level text in

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Overview

Providing the first comprehensive treatment of the subject, this groundbreaking work is solidly founded on a decade of concentrated research, some of which is published here for the first time, as well as practical, ''hands on'' classroom experience. The clarity of presentation and abundance of examples and exercises make it suitable as a graduate level text in mathematics, decision making, artificial intelligence, and engineering courses.

Product Details

ISBN-13:
9780306442605
Publisher:
Springer US
Publication date:
01/31/1993
Edition description:
1992
Pages:
354
Product dimensions:
6.10(w) x 9.25(h) x 0.03(d)

Related Subjects

Table of Contents

Ch. 1Introduction1
Ch. 2Required Background in Set Theory7
2.1Set Inclusion and Characteristic Function7
2.2Operations on Sets9
2.3Classes of Sets15
2.4Atoms and Holes22
2.5S-Compact Spaces28
2.6Relations, Posets, and Lattices30
Ch. 3Fuzzy Measures39
3.1Fuzzy Measures and Semicontinuous Fuzzy Measures39
3.2[lambda]-Fuzzy Measures42
3.3Quasi-measures50
3.4Belief Measures and Plausibility Measures54
3.5Possibility Measures and Necessity Measures62
3.6Properties of Finite Fuzzy Measures66
Ch. 4Extensions73
4.1Extension of Quasi-Measures and [lambda]-Fuzzy Measures73
4.2Extension of Semicontinuous Fuzzy Measures78
4.3Absolute Continuity and Extension of Fuzzy Measures81
4.4Extension of Possibility Measures and Necessity Measures84
Ch. 5Structural Characteristics for Set Functions95
5.1Null-Additivity95
5.2Autocontinuity97
5.3Uniform Autocontinuity106
5.4Structural Characteristics of Monotone Set Functions107
5.5Fuzzy Measures on S-Compact Spaces110
Ch. 6Measurable Functions on Fuzzy Measure Spaces115
6.1Measurable Functions115
6.2"Almost" and "Pseudo-Almost"117
6.3Relation Among Convergence of Measurable Function Sequence120
6.4Convergence of Measurable Function Sequence on Possibility Measure Spaces126
Ch. 7Fuzzy Integrals131
7.1Definition131
7.2Properties of the Fuzzy Integral135
7.3Convergence Theorems of the Fuzzy Integral Sequence143
7.4Transformation Theorem for Fuzzy Integrals152
7.5Fuzzy Measures Defined by Fuzzy Integrals154
7.6Fuzzy Integrals with Respect to a Nonnegative Monotone Set Function157
Ch. 8Pan-Integrals163
8.1Pan-Additions and Pan-Multiplications163
8.2Definition of Pan-Integral164
8.3Properties of Pan-Integral168
8.4A Transformation Theorem170
Ch. 9Applications175
9.1General Remarks175
9.2Dempster-Shafer Theory176
9.3Possibility Theory181
9.4Fuzzy Measures and Fuzzy Integrals184
9.5Fuzzy Convolution of Fuzzy Distributions190
References195
Appendix A. Some Concepts and Results Regarding Classical Measures203
Appendix B. Some Concepts and Results Regarding Fuzzy Sets209
Appendix C. Glossary of Key Concepts219
Appendix D. Glossary of Symbols227
Appendix E. New Directions in Fuzzy Measure Theory231
Appendix F. Representative Applications of Fuzzy Measure Theory285
Author Index343
Subject Index347

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