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Fuzzy Data Analysis : THEORY AND DECISION LIBRARY SERIES B, MATHEMATICAL AND STATISTICAL METHODS - Hans Bandemer

Fuzzy Data Analysis

THEORY AND DECISION LIBRARY SERIES B, MATHEMATICAL AND STATISTICAL METHODS

Hardcover Published: 30th June 1992
ISBN: 9780792317722
Number Of Pages: 343

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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.

Introductionp. 1
Basic notionsp. 9
Fuzzy setsp. 9
Set-theoretic operationsp. 13
Special fuzzy setsp. 19
Extension principle and applicationsp. 24
Fuzzy relationsp. 33
Fuzzy functionsp. 40
Measuring the uncertaintyp. 44
Basic notions of data analysisp. 61
Datap. 61
Grouping and transformationsp. 63
Similarity and distancesp. 64
Cluster analysisp. 73
Evaluation of functional relationshipsp. 79
Projection techniquesp. 82
Fuzzy datap. 89
Simple fuzzy datap. 89
Complex fuzzy datap. 98
Simple operations and transformationsp. 108
Qualitative analysisp. 121
Fuzzy clusteringp. 122
Similarity of fuzzy datap. 127
Fuzzy similarity of fuzzy datap. 145
Shape similarityp. 160
Quantitative analysisp. 185
Preliminary operationsp. 185
Local functional approximationp. 188
Global evaluationp. 191
Global approximation of fuzzy datap. 207
Some fuzzy counterpartsp. 215
Minimization of fuzzy functionsp. 230
Evaluation of methodsp. 241
Towards a normative theoryp. 242
Truth evaluationp. 251
Possibility evaluationp. 263
Probability evaluationp. 273
Fuzzy measure evaluationp. 300
Bibliographyp. 307
Subject Indexp. 327
List of Symbolsp. 339
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792317722
ISBN-10: 0792317726
Series: THEORY AND DECISION LIBRARY SERIES B, MATHEMATICAL AND STATISTICAL METHODS
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 343
Published: 30th June 1992
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 24.77 x 17.15  x 1.91
Weight (kg): 0.75