Fuzzy Data Analysis

1992
ISBN: 978-0-7923-1772-2
Verlag: Springer Netherlands

Buch, Englisch, Band 20, 343 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 1500 g

Reihe: Theory and Decision Library B

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.

Zielgruppe

Research

Autoren/Hrsg.

Näther, Wolfgang

Bandemer, Hans

Bandemer, H.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe

Inhaltsverzeichnis

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.