Overview

Fuzzy data such as marks, scores, verbal evaluations, imprecise observations, experts' opinions and grey tone pictures, are common. In ""Fuzzy Data Analysis"" the authors collect their results, aiming to provide the reader with ideas, approaches and methods for processing such data when looking for sub-structures in knowledge basis for an evaluation of functional relationship, for example in order to specify diagnostic of 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.

Full Product Details

Author:   Hans Bandemer ,  Wolfgang Näther
Publisher:   Springer
Imprint:   Springer
Edition:   1992 ed.
Volume:   20
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   1.500kg
ISBN:  

9780792317722

ISBN 10:   0792317726
Pages:   343
Publication Date:   30 June 1992
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Introduction.- 2 Basic notions.- 2.1 Fuzzy sets.- 2.2 Set-theoretic operations.- 2.3 Special fuzzy sets.- 2.4 Extension principle and applications.- 2.5 Fuzzy relations.- 2.6 Fuzzy functions.- 2.7 Measuring the uncertainty.- 3 Basic notions of data analysis.- 3.1 Data.- 3.2 Grouping and transformations.- 3.3 Similarity and distances.- 3.4 Cluster analysis.- 3.5 Evaluation of functional relationships.- 3.6 Projection techniques.- 4 Fuzzy data.- 4.1 Simple fuzzy data.- 4.2 Complex fuzzy data.- 4.3 Simple operations and transformations.- 5 Qualitative analysis.- 5.1 Fuzzy clustering.- 5.2 Similarity of fuzzy data.- 5.3 Fuzzy similarity of fuzzy data.- 5.4 Shape similarity.- 6 Quantitative analysis.- 6.1 Preliminary operations.- 6.2 Local functional approximation.- 6.3 Global evaluation.- 6.4 Global approximation of fuzzy data.- 6.5 Some fuzzy counterparts.- 6.6 Minimization of fuzzy functions.- 7 Evaluation of methods.- 7.1 Towards a normative theory.- 7.2 Truth evaluation.- 7.3 Possibility evaluation.- 7.4 Probability evaluation.- 7.5 Fuzzy measure evaluation.- List of Symbols.

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