Aggregation Functions (Encyclopedia of Mathematics and its Applications)
Cambridge University Press, 7/9/2009
EAN 9780521519267, ISBN10: 0521519268
Hardcover, 482 pages, 23.4 x 15.6 x 2.7 cm
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.
Preface
1. Introduction
2. Properties for aggregation
3. Conjunctive and disjunctive aggregation functions
4. Means and averages
5. Aggregation functions based on nonadditive integrals
6. Construction methods
7. Aggregation on specific scale types
8. Aggregation on ordinal scales
9. Aggregation on bipolar scales
10. Behavioral analysis of aggregation functions
11. Identification of aggregation functions
A. Aggregation of infinitely many arguments
B. Examples and applications
List of symbols
Bibliography
Index.
'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, Reviews.com