{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T05:27:43Z","timestamp":1740202063295,"version":"3.37.3"},"reference-count":0,"publisher":"IOS Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2008]]},"abstract":"<jats:p>In this paper a matrix representation for discrete quasi-copulas defined on a non-square grid In&amp;times; Imof [0,1]2with m=kn, k&amp;ge;1 is given. The special case of irreducible discrete quasi-copulas (those that cannot be expressed as nontrivial convex combination of other ones) is also studied. It is proved that quasi-copulas of minimal range admit a matrix representation through a special class of matrices. In the case of copulas, it is proved that irreducible copulas coincide with those of minimal range. Moreover, an algorithm to express any discrete copula as a convex combination of irreducible ones is given.<\/jats:p>","DOI":"10.3233\/978-1-58603-925-7-273","type":"book-chapter","created":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:26:53Z","timestamp":1740133613000},"source":"Crossref","is-referenced-by-count":0,"title":["Representation of discrete quasi-copulas through non-square matrices"],"prefix":"10.3233","author":[{"family":"Aguil&oacute; Isabel","sequence":"additional","affiliation":[]},{"family":"Su&ntilde;er Jaume","sequence":"additional","affiliation":[]},{"family":"Torrens Joan","sequence":"additional","affiliation":[]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","Artificial Intelligence Research and Development"],"original-title":[],"deposited":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:13:43Z","timestamp":1740136423000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospressISSNISBN&issn=0922-6389&volume=184&spage=273"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008]]},"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/978-1-58603-925-7-273","relation":{},"ISSN":["0922-6389"],"issn-type":[{"value":"0922-6389","type":"print"}],"subject":[],"published":{"date-parts":[[2008]]}}}