Book: Fuzzy Sets and Approximate Reasoning

Ruan Da (druan@sckcen.be)
Fri, 9 Apr 1999 15:11:04 +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
> Softercover, US$ 25 (inluded post fee)
>
> If you want to order 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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