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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.
Table des matières
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.
