Fuzzy Sets and Systems 142 (2004) 3–14 www.elsevier.com/locate/fss Measure-based aggregation operators Erich Peter Klement a ; ∗ , Radko Mesiar b; c , Endre Pap d a Department of Algebra, Stochastics and Knowledge-Based Mathematical Systems, Johannes Kepler University, 4040 Linz, Austria b Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak Technical University, 81368 Bratislava, Slovakia c Institute of Information Theory and Automation, Czech Academy of Sciences, Prague, Czech Republic d Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia and Montenegro Abstract In analogy to the representation of the standard probabilistic average as an expected value of a random variable, a geometric approach to aggregation is proposed, generalizing Imaoka’s integral based on copulas. Several properties of such aggregation operators are investigated, and the relationship with distinguished classes of aggregation operators is discussed. c  2003 Elsevier B.V. All rights reserved. Keywords: Aggregation operator; Fuzzy measure; Choquet integral; Triangular norm 1. Introduction Given a probability space (X; A;P), standard probabilistic averaging is done by means of the expected value of a random variable  : X → [0; 1] via E()=  1 0 P({ ¿ t })dt: (1) Similarly, the mean value of an integrable function f : [0; 1] → [0; 1] is given by E(f)=  1 0 ({f ¿ t })dt; (2) where  is the Lebesgue measure on R. * Corresponding author. Tel.: +43-732-2468-9151; fax: +43-732-2468-1351. E-mail addresses: ep.klement@jku.at (E.P. Klement), mesiar@math.sk (R. Mesiar), pap@im.ns.ac.yu, pape@eunet.yu (E. Pap). 0165-0114/$ - see front matter c  2003 Elsevier B.V. All rights reserved. doi:10.1016/j.fss.2003.10.028