Aggregation Functions

by Michel Grabisch, Jean-Luc Marichal, Radko Mesiar, Endre Pap

Overview

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.

Product Details

ISBN-13:	9780521519267
Publisher:	Cambridge University Press
Publication date:	07/09/2009
Series:	Encyclopedia of Mathematics and its Applications , #127
Pages:	482
Product dimensions:	6.00(w) x 9.30(h) x 1.50(d)

About the Author

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.

Table of Contents

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.

Editorial Reviews

"The book is very impressive in its scope. 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

"... it provides a very complete bibliography where applications and more details can be found. I find the book a complete and interesting guide for those who are interested in aggregation operators or need a guide to understand the main aspects of different operators."
Pedro Miranda, Mathematical Reviews

From the Publisher