{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T06:51:40Z","timestamp":1768719100313,"version":"3.49.0"},"reference-count":47,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2012,4,20]],"date-time":"2012-04-20T00:00:00Z","timestamp":1334880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Several discrete universal integrals on finite universes are discussed from an axiomatic point of view. We start from the first attempt due to B. Riemann and cover also most recent approaches based on level dependent capacities. Our survey includes, among others, the Choquet and the Sugeno integral and general copula-based integrals.<\/jats:p>","DOI":"10.3390\/axioms1010009","type":"journal-article","created":{"date-parts":[[2012,4,20]],"date-time":"2012-04-20T11:01:48Z","timestamp":1334919708000},"page":"9-20","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Discrete Integrals and Axiomatically Defined Functionals"],"prefix":"10.3390","volume":"1","author":[{"given":"Erich Peter","family":"Klement","sequence":"first","affiliation":[{"name":"Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Altenbergerstra\u00dfe 69, Linz, Austria"}]},{"given":"Radko","family":"Mesiar","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinsk\u00e9ho 11, Bratislava, Slovakia"}]}],"member":"1968","published-online":{"date-parts":[[2012,4,20]]},"reference":[{"key":"ref_1","unstructured":"Kepler, J. 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