{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T20:04:05Z","timestamp":1771617845184,"version":"3.50.1"},"reference-count":73,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,4]],"date-time":"2022-03-04T00:00:00Z","timestamp":1646352000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, a new hybrid model named linear Diophantine fuzzy rough set (LDFRS) is proposed to magnify the notion of rough set (RS) and linear Diophantine fuzzy set (LDFS). Concerning the proposed model of LDFRS, it is more efficient to discuss the fuzziness and roughness in terms of linear Diophantine fuzzy approximation spaces (LDFA spaces); it plays a vital role in information analysis, data analysis, and computational intelligence. The concept of (&lt;p,p\u2032&gt;,&lt;q,q\u2032&gt;)-indiscernibility of a linear Diophantine fuzzy relation (LDF relation) is used for the construction of an LDFRS. Certain properties of LDFA spaces are explored and related results are developed. Moreover, a decision-making technique is developed for modeling uncertainties in decision-making (DM) problems and a practical application of fuzziness and roughness of the proposed model is established for medical diagnosis.<\/jats:p>","DOI":"10.3390\/sym14030525","type":"journal-article","created":{"date-parts":[[2022,3,6]],"date-time":"2022-03-06T20:40:02Z","timestamp":1646599202000},"page":"525","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Linear Diophantine Fuzzy Rough Sets: A New Rough Set Approach with Decision Making"],"prefix":"10.3390","volume":"14","author":[{"given":"Saba","family":"Ayub","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}]},{"given":"Muhammad","family":"Shabir","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8115-9168","authenticated-orcid":false,"given":"Muhammad","family":"Riaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of the Punjab, Lahore 54590, Pakistan"}]},{"given":"Waqas","family":"Mahmood","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9657-0889","authenticated-orcid":false,"given":"Darko","family":"Bozanic","sequence":"additional","affiliation":[{"name":"Military Academy, University of Defence in Belgrade, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3583-9434","authenticated-orcid":false,"given":"Dragan","family":"Marinkovic","sequence":"additional","affiliation":[{"name":"Faculty of Mechanical Engineering, University of Nis, 18000 Nis, Serbia"},{"name":"Faculty of Mechanical Engineering and Transport Systems, TU Berlin, 10623 Berlin, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. 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