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Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. These functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer science, and many applied fields (economics and finance, pattern recognition and image processing, data fusion, etc.). This is a comprehensive, rigorous and self-contained exposition of aggregation functions. Classes of aggregation functions covered include triangular norms and conorms, copulas, means and averages, and those based on nonadditive integrals. The properties of each method, as well as their interpretation and analysis, are studied in depth, together with construction methods and practical identification methods. Special attention is given to the nature of scales on which values to be aggregated are defined (ordinal, interval, ratio, bipolar). It is an ideal introduction for graduate students and a unique resource for researchers.

Aggregation operators --- Numerical functions. --- Aggregation operators. --- wiskundige functies --- Numerical functions --- Functions, Numerical --- Numerical aggregation operators --- Operator theory

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Most of the observable phenomena in the empirical sciences are of a multivariate nature.In financial studies, assets in stock markets are observed simultaneously and their joint development is analyzed to better understand general tendencies and to track indices. In medicine recorded observations of subjects in different locations are the basis of reliable diagnoses and medication. In quantitative marketing consumer preferences are collected in order to construct models of consumer behavior. The underlying theoretical structure of these and many other quantitative studies of applied sciences is multivariate. Focussing on applications this book presents the tools and concepts of multivariate data analysis in a way that is understandable for non-mathematicians and practitioners who face statistical data analysis. In this second edition a wider scope of methods and applications of multivariate statistical analysis is introduced. All quantlets have been translated into the R and Matlab language and are made available online.

Multivariate analysis --- Analyse multivariée --- Multivariate analysis. --- Mathematical Statistics --- Mathematics --- Physical Sciences & Mathematics --- 519.2 --- 519.237 --- multivariaat --- wiskundige functies --- wiskundige statistiek --- Multivariate distributions --- Multivariate statistical analysis --- Statistical analysis, Multivariate --- Analysis of variance --- Mathematical statistics --- Matrices --- Probability. Mathematical statistics --- Multivariate statistical methods --- 519.237 Multivariate statistical methods --- 519.2 Probability. Mathematical statistics --- Analyse multivariée --- EPUB-LIV-FT LIVSTATI SPRINGER-B --- Mathematics. --- Economics, Mathematical. --- Probabilities. --- Statistics. --- Economic theory. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Quantitative Finance. --- Statistics for Business/Economics/Mathematical Finance/Insurance. --- Distribution (Probability theory. --- Mathematical statistics. --- Finance. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Funding --- Funds --- Economics --- Currency question --- Economic theory --- Political economy --- Social sciences --- Economic man --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics . --- Economics, Mathematical . --- Mathematical economics --- Probability --- Combinations --- Chance --- Least squares --- Risk --- Methodology