Fuzzy Sets and Approximate Reasoning

Huang Chongfu (hchongfu@email.bnu.edu.cn)
Wed, 7 Apr 1999 16:25:30 +0200 (MET DST)

Book announcement:
FUZZY SETS AND APPROXIMATE REASONING
(English Edition)

by Etienne E. Kerre ( University of Ghent, Belgium)

Xian Jiaotong University Press, China
Jan. 1999, 254pp
Softcover, US$ 25 (inluded post fee)

If you want to buy this book, please contact: (before June 1999)
Dr. Huang Chongfu
Institute of Resource Sciences
Beijing Normal University
Beijing 100875, China
E-mail: hchongfu98@bnu.edu.cn

This book highlights an essential selection of the basic concepts
and techniques of fuzzy sets theory and approximate reasoning as a
suitable tool for description of imprecision and uncertainty.
Special attentions of the book have been paid to the theoretical
foundation of fuzzy sets theory and approximate reasoning, as well
as a clear link to the practical use of fuzzy sets theory. The book,
culminated with Prof Kerre's over 20-year experience on
researching and teaching fuzzy sets theory, is suitable
for mathematicians, computer scientists, and engineers as either a
textbook or reference book.

Contents:
Foreword ..................................................................I
Preface...................................................................IV
Chapter 1 Some Preliminary Notions from Lattice Theory.....................1
1.1 Posets...............................................................1
1.2 Lattices.............................................................3
1.3 Boolean algebra......................................................6
Chapter 2 On the Concept of a Fuzzy Set and its Generalizations...........11
2.1 Introduction........................................................11
2.2 Definitions.........................................................14
2.3 Morgan algebra of fuzzy sets in some universe.......................14
2.4 Alternative operations on F(X)......................................19
2.5 Zadeh's operations in terms of fuzzy singletons.....................23
2.6 On weak and strong a-levels.........................................25
2.7 Flou sets, n-flou sets..............................................28
2.8 L-fuzzy sets, L-flou sets...........................................31
2.9 Some typical membership functions...................................42
2.10 Cartesian product of fuzzy sets....................................44
2.11 Modifying operations on fuzzy sets.................................49
2.12 Images of fuzzy sets under ordinary mappings.......................59
2.13 Bounded fuzzy sets on $R^n$........................................67
2.14 Convex fuzzy sets..................................................71
2.15 Index of fuzziness.................................................79
Chapter 3 Fuzzy Relations.................................................86
3.1 Introduction........................................................86
3.2 Definitions.........................................................92
3.3 Operations between fuzzy relations..................................94
3.4 Composition of fuzzy relations......................................96
3.5 Fuzzy relations and convexity......................................107
3.6 Projections and cylindrical extensions of fuzzy relations..........111
3.7 Special kinds of fuzzy binary relations on a set...................115
Chapter 4 A Survey of Fuzzy Connectives..................................130
4.1 Introduction.......................................................130
4.2 Definition of fuzzy connectives....................................135
4.3 Duality principle..................................................137
4.4 A list of dual binary operations...................................138
4.5 Properties of fuzzy connectives....................................139
4.6 Experimental results...............................................145
Chapter 5 Calculus of Fuzzy Quantities...................................148
5.1 Introduction.......................................................148
5.2 Definitions........................................................149
5.3 Some additional properties with respect to $\alpha $-levels........150
5.4 Some topological reflections.......................................152
5.5 Unary operations on fuzzy quantities...............................154
5.6 Binary operations on fuzzy quantities..............................156
5.7 Computer-representation of fuzzy quantities........................159
5.8 Algorithm for the implementation of binary operations on
piecewise linear fuzzy quantities with bounded support.............164
5.9 Comparison with existing methods...................................168
5.10 Application to approximate reasoning techniques in fuzzy
expert systems....................................................169
Chapter 6 Measures of Uncertainty - Fuzzy Measures.......................171
6.1 Introduction.......................................................171
6.2 Fuzzy measures.....................................................177
6.3 Special fuzzy measures.............................................184
6.4 Representation of imprecision......................................204
Chapter 7 Description of an Expert System Shell Based on
Fuzzy truth values.............................................209
7.1 Formal description of classical expert systems.....................209
7.2 Formal description of a fuzzy expert system........................215
7.3 Short description of FDL...........................................229
7.4 Short description of EDL...........................................235
Reference................................................................242
Author...................................................................254

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