{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T05:49:58Z","timestamp":1778824198725,"version":"3.51.4"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Ltd","issue":"Suppl. 2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Unc. Fuzz. Knowl. Based Syst."],"published-print":{"date-parts":[[2018,12]]},"abstract":"<jats:p>In this paper we present a new approach to rough set approximations that permits to distinguish between two kinds of \u201cimperfect\u201d knowledge in a joint framework: on one hand, vagueness, due to imprecise knowledge and uncertainty typical of fuzzy sets, and on the other hand, ambiguity, due to granularity of knowledge originating from the coarseness typical of rough sets. The basic idea of our approach is that each concept is represented by an orthopair, that is, a pair of disjoint sets in the universe of knowledge. The first set in the pair contains all the objects that are considered as surely belonging to the concept, while the second set contains all the objects that surely do not belong to the concept. In this context, following some previous research conducted by us on the algebra of rough sets, we propose to define as rough approximation of the orthopair representing the considered concept another orthopair composed of lower approximations of the two sets in the first orthopair. We shall apply this idea to the classical rough set approach based on indiscernibility, as well as to the dominance-based rough set approach. We discuss also a variable precision rough approximation, and a fuzzy rough approximation of the orthopairs. Some didactic examples illustrate the proposed methodology.<\/jats:p>","DOI":"10.1142\/s0218488518400135","type":"journal-article","created":{"date-parts":[[2018,12,20]],"date-time":"2018-12-20T03:07:35Z","timestamp":1545275255000},"page":"89-125","source":"Crossref","is-referenced-by-count":6,"title":["Distinguishing Vagueness from Ambiguity in Rough Set Approximations"],"prefix":"10.1142","volume":"26","author":[{"given":"Salvatore","family":"Greco","sequence":"first","affiliation":[{"name":"Department of Economics and Business, University of Catania, 95129 Catania, Italy"},{"name":"Portsmouth Business School, Centre of Operations Research and Logistics (CORL), University of Portsmouth, Portsmouth PO1 3DE, United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benedetto","family":"Matarazzo","sequence":"additional","affiliation":[{"name":"Department of Economics and Business, University of Catania, 95129 Catania, Italy"},{"name":"Department of Law, LUMSA University, Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5200-7795","authenticated-orcid":false,"given":"Roman","family":"S\u0142owi\u0144ski","sequence":"additional","affiliation":[{"name":"Institute of Computing Science, Pozna\u0144 University of Technology, 60-965 Pozna\u0144, Poland"},{"name":"Systems Research Institute, Polish Academy of Sciences, 01-447 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,1,30]]},"reference":[{"key":"p_33","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"p_36","first-page":"203","author":"Dubois D.","year":"1992","journal-title":"Dordrecht"},{"key":"p_37","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(01)00032-X"},{"key":"p_39","first-page":"106","author":"Pawlak Z.","year":"1997","journal-title":"Heidelberg"},{"key":"p_40","first-page":"1","author":"Pawlak Z.","year":"2005","journal-title":"Berlin"},{"key":"p_41","doi-asserted-by":"publisher","DOI":"10.1007\/s41066-015-0013-y"},{"key":"p_42","first-page":"1","volume":"39","author":"Monteiro A.","year":"1980","journal-title":"Portugaliae Mathematica"},{"key":"p_43","doi-asserted-by":"publisher","DOI":"10.1109\/3477.658584"},{"key":"p_44","first-page":"127","author":"Cattaneo G.","year":"2009","journal-title":"Amsterdam"},{"key":"p_45","doi-asserted-by":"publisher","DOI":"10.1109\/ICCI.1993.315346"},{"key":"p_46","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90239-X"},{"key":"p_47","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(00)00167-3"},{"key":"p_48","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(01)00244-2"},{"key":"p_49","doi-asserted-by":"publisher","DOI":"10.1002\/int.10014"},{"key":"p_50","first-page":"624","author":"Greco S.","year":"2012","journal-title":"Berlin"},{"key":"p_52","first-page":"81","author":"Greco S.","year":"2017","journal-title":"Cham"},{"key":"p_53","first-page":"557","author":"Slowi\u0144ski R.","year":"2014","journal-title":"New York"},{"key":"p_54","doi-asserted-by":"crossref","first-page":"25","DOI":"10.3233\/FI-2012-639","volume":"115","author":"Greco S.","year":"2012","journal-title":"Fundamenta Informaticae"},{"issue":"4","key":"p_55","first-page":"969","volume":"29","author":"Susmaga R.","year":"2000","journal-title":"Control and Cybernetics"},{"key":"p_56","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(93)90048-2"},{"key":"p_58","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2009.02.011"},{"key":"p_60","first-page":"283","author":"Greco S.","year":"1998","journal-title":"Berlin"},{"key":"p_61","first-page":"14","author":"Greco S.","year":"1999","journal-title":"Boston"},{"key":"p_62","first-page":"149","author":"Greco S.","year":"2000","journal-title":"Berlin"},{"key":"p_63","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"p_64","first-page":"343","volume":"20","author":"D","year":"1996","journal-title":"Turkish Journal of Mathematics"},{"key":"p_65","doi-asserted-by":"publisher","DOI":"10.1111\/1468-0394.00250"},{"key":"p_67","first-page":"131","author":"Greco S.","year":"2000","journal-title":"Heidelberg"},{"key":"p_68","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.12.009"}],"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\/S0218488518400135","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,18]],"date-time":"2020-11-18T09:56:18Z","timestamp":1605693378000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218488518400135"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12]]},"references-count":29,"journal-issue":{"issue":"Suppl. 2","published-online":{"date-parts":[[2019,1,30]]},"published-print":{"date-parts":[[2018,12]]}},"alternative-id":["10.1142\/S0218488518400135"],"URL":"https:\/\/doi.org\/10.1142\/s0218488518400135","relation":{},"ISSN":["0218-4885","1793-6411"],"issn-type":[{"value":"0218-4885","type":"print"},{"value":"1793-6411","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12]]}}}