{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:13:31Z","timestamp":1758269611798},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2009,6]]},"abstract":"<jats:p> In this paper we study a generalization of a submeasure notion which is related to a probabilistic concept, especially to Menger spaces where triangular norms play a crucial role. The resulting notion of a \u03c4<jats:sub>T<\/jats:sub>-submeasure is suitable for modeling those situations in which we have only probabilistic information about the measure of the set. We characterize a class of universal \u03c4<jats:sub>T<\/jats:sub>-submeasures (i.e., \u03c4<jats:sub>T<\/jats:sub>-submeasures for an arbitrary t -norm T) and give explicit formulas for \u03c4<jats:sub>T<\/jats:sub>-submeasures for some classes of t -norms. Also, transformations and aggregations of \u03c4<jats:sub>T<\/jats:sub>-submeasures are discussed. <\/jats:p>","DOI":"10.1142\/s0218488509005887","type":"journal-article","created":{"date-parts":[[2009,6,5]],"date-time":"2009-06-05T05:34:12Z","timestamp":1244180052000},"page":"297-316","source":"Crossref","is-referenced-by-count":8,"title":["ON A CERTAIN CLASS OF SUBMEASURES BASED ON TRIANGULAR NORMS"],"prefix":"10.1142","volume":"17","author":[{"given":"ONDREJ","family":"HUTN\u00cdK","sequence":"first","affiliation":[{"name":"Institute of Mathematics, Faculty of Science, Pavol Jozef \u0160af\u00e1rik University in Ko\u0161ice, Jesenn\u00e1 5, 041 54 Ko\u0161ice, Slovakia"}]},{"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, 813 68 Bratislava, Slovakia"},{"name":"IRAFM University of Ostrava, 701 03 Ostrava, Czech Republic"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","volume-title":"Lectures on Functional Equations and their Applications","author":"Acz\u00e9l J.","year":"1966"},{"key":"rf2","first-page":"669","volume":"15","author":"Agafonova L. V.","journal-title":"Sibirsk. Mat. Zh."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/9789812774200"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044450263-6\/50024-5"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1787-4"},{"key":"rf6","first-page":"5","volume":"112","author":"Dobrakov I.","journal-title":"Dissertationes Math."},{"key":"rf7","first-page":"65","volume":"30","author":"Dobrakov I.","journal-title":"On submeasures II, Math. Slovaca"},{"key":"rf8","first-page":"269","volume":"20","author":"Drewnowski L.","journal-title":"Bull. Acad. Polon. Sci. Ser. Sci. Math., Astr. Phys."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-4429-6_11"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.03.019"},{"key":"rf11","volume-title":"Fuzzy Measures and Integrals. Theory and Applications","author":"Grabisch M.","year":"2000"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-1560-7"},{"key":"rf13","first-page":"149","volume":"40","author":"Halu\u0161ka J.","journal-title":"Tatra Mt. Math. Publ."},{"key":"rf15","volume-title":"Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms","author":"Klement E. P.","year":"2005"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9540-7"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.28.12.535"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.05.033"},{"key":"rf19","volume-title":"Null-Additive Set Functions","author":"Pap E.","year":"1995"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2004.07.004"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1142\/S0218488502001806"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-008-2936-8"},{"key":"rf23","first-page":"2092","volume":"247","author":"Schweizer B.","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A"},{"key":"rf24","series-title":"North-Holland Series in Probability and Applied Mathematics","volume-title":"Probabilistic Metric Spaces","author":"Schweizer B.","year":"1983"},{"key":"rf25","first-page":"3","volume":"124","author":"\u0160erstnev A. N.","journal-title":"Kazan Gos. Univ. U\u010den. Zap."}],"container-title":["International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218488509005887","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:13:12Z","timestamp":1565133192000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488509005887"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6]]},"references-count":24,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2009,6]]}},"alternative-id":["10.1142\/S0218488509005887"],"URL":"https:\/\/doi.org\/10.1142\/s0218488509005887","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6]]}}}