Aggregation functions: Construction methods, conjunctive, disjunctive and mixed classes

in Information Sciences (2011), 181(1), 23-43

In this second part of our state-of-the-art overview on aggregation theory, based again on our recent monograph on aggregation functions, we focus on several construction methods for aggregation functions ... [more ▼]

In this second part of our state-of-the-art overview on aggregation theory, based again on our recent monograph on aggregation functions, we focus on several construction methods for aggregation functions and on special classes of aggregation functions, covering the well-known conjunctive, disjunctive, and mixed aggregation functions. Some fields of applications are included. [less ▲]

Aggregation functions

Book published by Cambridge University Press (2009)

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 ... [more ▼]

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. [less ▲]

Contribution on some construction methods for aggregation functions

in Bodenhofer, Ulrich; De Baets, Bernard; Klement, Erich Peter (Eds.) et al Proc. 30th Linz Seminar on Fuzzy Set Theory (LINZ 2009): The Legacy of 30 Seminars – Where Do We Stand and Where Do We Go? (2009, February)

In this paper, based on [14], we present some well established construction methods for aggregation functions as well as some new ones.

Behavioral analysis of aggregation functions

in Bodenhofer, Ulrich; De Baets, Bernard; Klement, Erich Peter (Eds.) et al Proc. 30th Linz Seminar on Fuzzy Set Theory (LINZ 2009): The Legacy of 30 Seminars – Where Do We Stand and Where Do We Go? (2009, February)

“Aggregation Functions”, Cambridge University Press

in Proc. of the 6th Int. Symposium on Intelligent Systems and Informatics (SISY 2008) (2008, September)

There is given a short overview of the monograph ”Aggregation Functions” (M. Grabisch, J. L. Marichal, R. Mesiar, E. Pap), Cambridge University Press (in press).