{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:21:17Z","timestamp":1777645277125,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2015,8,1]],"date-time":"2015-08-01T00:00:00Z","timestamp":1438387200000},"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":[[2015,8]]},"abstract":"<jats:p>In this paper, we investigate properties of the lower and upper approximations of an S-approximation space under different assumptions for its S operator. These assumptions are partial monotonicity, complement compatibility and functional partial monotonicity. We also extend the theory of three way decisions to non-inclusion relations. Also in this work, a new representation for partial monotone S-approximation spaces, called inflections, is introduced. We will also discuss the computational complexity of representing an S-approximation space in terms of inflection sets. Finally, the usefulness of the introduced concepts is illustrated by an example.<\/jats:p>","DOI":"10.3233\/fi-2015-1236","type":"journal-article","created":{"date-parts":[[2015,7,14]],"date-time":"2015-07-14T14:24:30Z","timestamp":1436883870000},"page":"307-328","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":21,"title":["S-approximation Spaces: A Three-way Decision Approach"],"prefix":"10.1177","volume":"139","author":[{"given":"Ali","family":"Shakiba","sequence":"first","affiliation":[{"name":"Department of Computer Science, Yazd University, Yazd, Iran."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammad R.","family":"Hooshmandasl","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Yazd University, Yazd, Iran."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,8,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1236","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1236","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:50Z","timestamp":1777444310000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2015-1236"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2015,8]]}},"alternative-id":["10.3233\/FI-2015-1236"],"URL":"https:\/\/doi.org\/10.3233\/fi-2015-1236","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8]]}}}