This volume is a comprehensive, rigorous, and self-contained exposition of aggregation functions, which are used when combining several numerical values into a single representative value. Classes of aggregation functions covered include triangular norms and conorms, copulas, means and averages, and those based on nonadditive integrals. The authors provide in-depth descriptions of the properties of each method (including interpretation, analysis, construction methods, and practical identification methods) and pay special attention to the nature of scales on which values to be aggregated are defined. This book is an excellent introduction to the subject for graduate students and an essential reference for researchers. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
A rigorous and self-contained exposition of aggregation functions and their properties.
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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