TY  - GEN
AU  - Grabisch, Michel 
AU  - Marichal, Jean-Luc 
AU  - Mesiar, Radko 
AU  - Pap, Endre 
TI  - Aggregation functions, Vol.127
SN  - 9780521519267
U1  - 512 
PY  - 2009///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Numerical
KW  - Functions
KW  - Aggregation
KW  - Operators
KW  - scales
N2  - 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
ER  -