Fuzzy Data Analysis

By: Hans Bandemer, Wolfgang Nather

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Hardcover | 30 June 1992

At a Glance

Hardcover
360 Pages

Dimensions(cm)
24.1 x 16.9 x 2.7

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Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are quite common. In Fuzzy Data Analysis the authors collect their recent results providing the reader with ideas, approaches and methods for processing such data when looking for sub-structures in knowledge bases for an evaluation of functional relationship, e.g. in order to specify diagnostic or control systems. The modelling presented uses ideas from fuzzy set theory and the suggested methods solve problems usually tackled by data analysis if the data are real numbers.
Fuzzy Data Analysis is self-contained and is addressed to mathematicians oriented towards applications and to practitioners in any field of application who have some background in mathematics and statistics.

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You Can Find This Book In

Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Set Theory Probability & Statistics Calculus & Mathematical Analysis Applied Mathematics Fuzzy Set Theory Business & Management Operational Research

Introduction	p. 1
Basic notions	p. 9
Fuzzy sets	p. 9
Set-theoretic operations	p. 13
Special fuzzy sets	p. 19
Extension principle and applications	p. 24
Fuzzy relations	p. 33
Fuzzy functions	p. 40
Measuring the uncertainty	p. 44
Basic notions of data analysis	p. 61
Data	p. 61
Grouping and transformations	p. 63
Similarity and distances	p. 64
Cluster analysis	p. 73
Evaluation of functional relationships	p. 79
Projection techniques	p. 82
Fuzzy data	p. 89
Simple fuzzy data	p. 89
Complex fuzzy data	p. 98
Simple operations and transformations	p. 108
Qualitative analysis	p. 121
Fuzzy clustering	p. 122
Similarity of fuzzy data	p. 127
Fuzzy similarity of fuzzy data	p. 145
Shape similarity	p. 160
Quantitative analysis	p. 185
Preliminary operations	p. 185
Local functional approximation	p. 188
Global evaluation	p. 191
Global approximation of fuzzy data	p. 207
Some fuzzy counterparts	p. 215
Minimization of fuzzy functions	p. 230
Evaluation of methods	p. 241
Towards a normative theory	p. 242
Truth evaluation	p. 251
Possibility evaluation	p. 263
Probability evaluation	p. 273
Fuzzy measure evaluation	p. 300
Bibliography	p. 307
Subject Index	p. 327
List of Symbols	p. 339
Table of Contents provided by Blackwell. All Rights Reserved.

Fuzzy Data Analysis

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Hardcover

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