Aggregation Functions

Nonfiction, Computers, Advanced Computing, Natural Language Processing, Science & Nature, Mathematics, General Computing
Cover of the book Aggregation Functions by Michel Grabisch, Jean-Luc Marichal, Radko Mesiar, Endre Pap, Cambridge University Press
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Author: Michel Grabisch, Jean-Luc Marichal, Radko Mesiar, Endre Pap ISBN: 9781139636087
Publisher: Cambridge University Press Publication: July 9, 2009
Imprint: Cambridge University Press Language: English
Author: Michel Grabisch, Jean-Luc Marichal, Radko Mesiar, Endre Pap
ISBN: 9781139636087
Publisher: Cambridge University Press
Publication: July 9, 2009
Imprint: Cambridge University Press
Language: English

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.

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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.

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