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  1. Home
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  3. Aggregation Functions
  • Cited by 854
Publisher:
Cambridge University Press
Online publication date:
March 2013
Print publication year:
2009
Online ISBN:
9781139644150
DOI:
https://doi.org/10.1017/CBO9781139644150
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Computer Science, Artificial Intelligence and Natural Language Processing
Series:
Encyclopedia of Mathematics and its Applications (127)
Information

Book description

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.

Reviews

'Throughout the entire work, many examples and applications of aggregation are given. The presentation is abstract, formal, and mathematically rigorous, providing a firm foundation for specific applications. This book should be taken very seriously by anyone whose work involves aggregation.'

Jonathan Golan Source: Reviews.com

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