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Fuzzy Measure Theory - Zhenyuan Wang

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Published: 31st January 1993
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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.

Introductionp. 1
Required Background in Set Theoryp. 7
Set Inclusion and Characteristic Functionp. 7
Operations on Setsp. 9
Classes of Setsp. 15
Atoms and Holesp. 22
S-Compact Spacesp. 28
Relations, Posets, and Latticesp. 30
Fuzzy Measuresp. 39
Fuzzy Measures and Semicontinuous Fuzzy Measuresp. 39
[lambda]-Fuzzy Measuresp. 42
Quasi-measuresp. 50
Belief Measures and Plausibility Measuresp. 54
Possibility Measures and Necessity Measuresp. 62
Properties of Finite Fuzzy Measuresp. 66
Extensionsp. 73
Extension of Quasi-Measures and [lambda]-Fuzzy Measuresp. 73
Extension of Semicontinuous Fuzzy Measuresp. 78
Absolute Continuity and Extension of Fuzzy Measuresp. 81
Extension of Possibility Measures and Necessity Measuresp. 84
Structural Characteristics for Set Functionsp. 95
Null-Additivityp. 95
Autocontinuityp. 97
Uniform Autocontinuityp. 106
Structural Characteristics of Monotone Set Functionsp. 107
Fuzzy Measures on S-Compact Spacesp. 110
Measurable Functions on Fuzzy Measure Spacesp. 115
Measurable Functionsp. 115
"Almost" and "Pseudo-Almost"p. 117
Relation Among Convergence of Measurable Function Sequencep. 120
Convergence of Measurable Function Sequence on Possibility Measure Spacesp. 126
Fuzzy Integralsp. 131
Definitionp. 131
Properties of the Fuzzy Integralp. 135
Convergence Theorems of the Fuzzy Integral Sequencep. 143
Transformation Theorem for Fuzzy Integralsp. 152
Fuzzy Measures Defined by Fuzzy Integralsp. 154
Fuzzy Integrals with Respect to a Nonnegative Monotone Set Functionp. 157
Pan-Integralsp. 163
Pan-Additions and Pan-Multiplicationsp. 163
Definition of Pan-Integralp. 164
Properties of Pan-Integralp. 168
A Transformation Theoremp. 170
Applicationsp. 175
General Remarksp. 175
Dempster-Shafer Theoryp. 176
Possibility Theoryp. 181
Fuzzy Measures and Fuzzy Integralsp. 184
Fuzzy Convolution of Fuzzy Distributionsp. 190
Referencesp. 195
Appendix A. Some Concepts and Results Regarding Classical Measuresp. 203
Appendix B. Some Concepts and Results Regarding Fuzzy Setsp. 209
Appendix C. Glossary of Key Conceptsp. 219
Appendix D. Glossary of Symbolsp. 227
Appendix E. New Directions in Fuzzy Measure Theoryp. 231
Appendix F. Representative Applications of Fuzzy Measure Theoryp. 285
Author Indexp. 343
Subject Indexp. 347
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306442605
ISBN-10: 0306442604
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 354
Published: 31st January 1993
Publisher: Springer Science+Business Media
Country of Publication: US
Dimensions (cm): 24.13 x 16.51  x 3.18
Weight (kg): 0.66