Aggregation functions: Means

in Information Sciences (2011), 181(1), 1-22

This two-part state-of-the-art overview on aggregation theory summarizes the essential information concerning aggregation issues. An overview of aggregation properties is given, including the basic ... [more ▼]

This two-part state-of-the-art overview on aggregation theory summarizes the essential information concerning aggregation issues. An overview of aggregation properties is given, including the basic classification on aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with multiple arities (extended means). [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 ▲]

Infinitary aggregation

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 [12, 18], we present infinitary aggregation functions on sequences possessing some a priori given properties. General infinitary aggregation is also discussed, and the connection ... [more ▼]

In this paper, based on [12, 18], we present infinitary aggregation functions on sequences possessing some a priori given properties. General infinitary aggregation is also discussed, and the connection with integrals, e.g., Lebesgue, Choquet and Sugeno integrals, is given. [less ▲]

Aggregation on bipolar scales

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)

Monograph: aggregation functions

in Acta Polytechnica Hungarica (2009), 6(1), 79-94

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) with more details from introductory ... [more ▼]

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) with more details from introductory Chapters 1 and 2. [less ▲]

A complete description of comparison meaningful functions

in Montseny, Eduard; Sobrevilla, Pilar (Eds.) Proceedings of the Joint 4th Conference of the European Society for Fuzzy Logic and Technology and the 11th Rencontres Francophones sur la Logique Floue et ses Applications, Barcelona, Spain, September 7-9, 2005. (2005, September)

Comparison meaningful functions acting on some real interval E are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful ... [more ▼]

Comparison meaningful functions acting on some real interval E are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful functions is further specified. Several already known results for comparison meaningful functions and invariant functions are [less ▲]

A complete description of comparison meaningful functions

in Aequationes Mathematicae (2005), 69(3), 309-320

Comparison meaningful functions acting on some real interval E are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful ... [more ▼]

Comparison meaningful functions acting on some real interval E are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful functions is further specified. Several already known results for comparison meaningful functions and invariant functions are obtained as consequences of our description. [less ▲]

A complete description of comparison meaningful functions

in Bouyssou, Denis; Janowitz, Mel; Roberts, Fred (Eds.) et al Annales du LAMSADE No 3 - Octobre 2004 (2004, October)

Comparison meaningful functions acting on some real interval E are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful ... [more ▼]

Comparison meaningful functions acting on some real interval E are completely described as transformed coordinate projections on minimal invariant subsets. The case of monotone comparison meaningful functions is further specified. Several already known results for comparison meaningful functions and invariant functions are obtained as consequences of our description. [less ▲]

Aggregation on finite ordinal scales by scale independent functions

in Order: A Journal on the Theory of Ordered Sets and its Applications (2004), 21(2), 155-180

We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have ... [more ▼]

We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have discrete representatives when the ordinal scales are considered as totally ordered finite sets. We also show that those scale independent functions identify with the so-called order invariant functions, which have been described recently. In particular, this identification allows us to justify the continuity property for certain order invariant functions in a natural way. [less ▲]