Aggregation Functions: 127 (Encyclopedia of Mathematics and its Applications, Series Number 127)

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.

Michel Grabisch is a Professor of Computer Sciences at Université Paris I, Panthéon-Sorbonne.

Jean-Luc Marichal is an Associate Professor in the Mathematics Research Unit at the University of Luxembourg.

Radko Mesiar is Chairman of the Department of Mathematics and Descriptive Geometry at the Slovak University of Technology, Bratislava.

Endre Pap is a Professor in the Department of Mathematics and Informatics at the University of Novi Sad, Serbia.