{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:20:23Z","timestamp":1777645223490,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2015,5,1]],"date-time":"2015-05-01T00:00:00Z","timestamp":1430438400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2015,5]]},"abstract":"<jats:p>\n                    In this paper, we consider tolerances induced by irredundant coverings. Each tolerance R on U determines a quasiorder \u2264\n                    <jats:sub>R<\/jats:sub>\n                    by setting x \u2264\n                    <jats:sub>R<\/jats:sub>\n                    y if and only if R(x) \u2286 R(y). We prove that for a tolerance R induced by a covering H of U, the covering H is irredundant if and only if the quasiordered set (U,\u2264\n                    <jats:sub>R<\/jats:sub>\n                    ) is bounded by minimal elements and the tolerance R coincides with the product \u2265\n                    <jats:sub>R<\/jats:sub>\n                    \u00b0 \u2264\n                    <jats:sub>R<\/jats:sub>\n                    . We also show that in such a case H = {\u2191m | m is minimal in (U,\u2264\n                    <jats:sub>R<\/jats:sub>\n                    )}, and for each minimal m, we have R(m) = \u2191m. Additionally, this irredundant covering H inducing R consists of some blocks of the tolerance R. We give necessary and sufficient conditions under which H and the set of R-blocks coincide. These results are established by applying the notion of Helly numbers of quasiordered sets.\n                  <\/jats:p>","DOI":"10.3233\/fi-2015-1183","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T01:30:37Z","timestamp":1575336637000},"page":"341-353","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Tolerances Induced by Irredundant Coverings"],"prefix":"10.1177","volume":"137","author":[{"given":"Jouni","family":"J\u00e4rvinen","sequence":"first","affiliation":[{"name":"Sirkankuja 1, 20810 Turku, Finland. Jouni.Kalervo.Jarvinen@gmail.com"}]},{"given":"S\u00e1ndor","family":"Radeleczki","sequence":"additional","affiliation":[{"name":"Sirkankuja 1, 20810 Turku, Finland. Jouni.Kalervo.Jarvinen@gmail.com"}]}],"member":"179","published-online":{"date-parts":[[2015,5,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1183","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1183","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:41Z","timestamp":1777444301000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2015-1183"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,5]]}},"alternative-id":["10.3233\/FI-2015-1183"],"URL":"https:\/\/doi.org\/10.3233\/fi-2015-1183","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,5]]}}}