{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,2]],"date-time":"2025-07-02T04:11:06Z","timestamp":1751429466026,"version":"3.41.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["FI"],"published-print":{"date-parts":[[2021,3,10]]},"abstract":"<jats:p>The paper contains some remarks on building automated counterpart of a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to arbitrary binary relation. Our focus was on translating rationality postulates for such operators by means of the Mizar system \u2013 the software and the database which allows for expressing and checking mathematical knowledge for the logical correctness. The main objective was the formal (and machine-checked) proof of Theorem 4.1 from A. Gomoli\u0144ska\u2019s paper \u201cA Comparative Study of Some Generalized Rough Approximations\u201d, hence the present title. We provide also the discussion on how to make the presentation more efficient to reuse the reasoning techniques of the Mizar verifier.<\/jats:p>","DOI":"10.3233\/fi-2021-2019","type":"journal-article","created":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T15:57:45Z","timestamp":1615564665000},"page":"165-182","source":"Crossref","is-referenced-by-count":2,"title":["Automated Comparative Study of Some Generalized Rough Approximations"],"prefix":"10.1177","volume":"179","author":[{"given":"Adam","family":"Grabowski","sequence":"first","affiliation":[{"name":"Institute of Informatics, University of Bia\u0142ystok, Konstantego Cio\u0142kowskiego 1M, 15-245 Bia\u0142ystok, Poland. adam@math.uwb.edu.pl"}]}],"member":"179","container-title":["Fundamenta Informaticae"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/FI-2021-2019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:56:21Z","timestamp":1751367381000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/FI-2021-2019"}},"subtitle":[],"editor":[{"given":"H.","family":"Schlingloff","sequence":"additional","affiliation":[]},{"given":"W.","family":"Penczek","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,3,10]]},"references-count":0,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.3233\/fi-2021-2019","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"type":"print","value":"0169-2968"},{"type":"electronic","value":"1875-8681"}],"subject":[],"published":{"date-parts":[[2021,3,10]]}}}