{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:47:37Z","timestamp":1777704457340,"version":"3.51.4"},"reference-count":24,"publisher":"SAGE Publications","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2020,11,19]]},"abstract":"<jats:p>In this paper, we join the notion of fuzzy ideal to the notion of fuzzy approximation space to define the notion of fuzzy ideal approximation spaces. We introduce the fuzzy ideal approximation interior operator int \u03a6 \u03bb and the fuzzy ideal approximation closure operator cl \u03a6 \u03bb , and moreover, we define the fuzzy ideal approximation preinterior operator p int \u03a6 \u03bb and the fuzzy ideal approximation preclosure operator p cl \u03a6 \u03bb with respect to that fuzzy ideal defined on the fuzzy approximation space (X, R) associated with some fuzzy set \u03bb\u00a0\u2208\u00a0IX. Also, we define fuzzy separation axioms, fuzzy connectedness and fuzzy compactness in fuzzy approximation spaces and in fuzzy ideal approximation spaces as well, and prove the implications in between.<\/jats:p>","DOI":"10.3233\/jifs-192072","type":"journal-article","created":{"date-parts":[[2020,9,29]],"date-time":"2020-09-29T15:48:58Z","timestamp":1601394538000},"page":"6869-6880","source":"Crossref","is-referenced-by-count":2,"title":["Fuzzy roughness via ideals"],"prefix":"10.1177","volume":"39","author":[{"given":"S. H.","family":"Alsulami","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Jeddah, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ismail","family":"Ibedou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. E.","family":"Abbas","sequence":"additional","affiliation":[{"name":"Department of Mathematicss, Faculty of Science, Sohag University, Sohag, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-192072_ref1","doi-asserted-by":"crossref","unstructured":"Akram M. , Fuzzy Lie Algebras, Infosys Science Foundation Series in Mathematical Sciences, Springer, (2018).","DOI":"10.1007\/978-981-13-3221-0"},{"issue":"1-2","key":"10.3233\/JIFS-192072_ref2","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1023\/A:1026773308067","article-title":"Idealization of some weak separation axioms","volume":"89","author":"Arenas","year":"2000","journal-title":"Acta Math Hung"},{"issue":"3","key":"10.3233\/JIFS-192072_ref3","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/s10474-005-0241-8","article-title":"On decompositions of continuity and some weaker forms of continuity via idealization","volume":"109","author":"Aslim","year":"2005","journal-title":"Acta Math Hung"},{"key":"10.3233\/JIFS-192072_ref4","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/0022-247X(81)90003-2","article-title":"Fuzzy grills and a characterization of fuzzy proximity","volume":"79","author":"Azad","year":"1981","journal-title":"J Math Anal Appl"},{"key":"10.3233\/JIFS-192072_ref5","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1016\/0022-247X(68)90057-7","article-title":"Fuzzy topological spaces","volume":"24","author":"Chang","year":"1968","journal-title":"J of Math Anal Appl"},{"key":"10.3233\/JIFS-192072_ref6","first-page":"171","article-title":"Sur les notions de filter et grill","volume":"224","author":"Choquet","year":"1947","journal-title":"Comptes Rendus Acad Sci Paris"},{"key":"10.3233\/JIFS-192072_ref7","first-page":"157","volume-title":"On rough sets in topological Boolean algebra","author":"Chuchro","year":"1994"},{"key":"10.3233\/JIFS-192072_ref9","first-page":"863","article-title":"Ideals in topological spaces and the set operatory","volume":"7","author":"Hamlett","year":"1990","journal-title":"Bollettino dell\u2019Unione Matematica Italiana"},{"issue":"1","key":"10.3233\/JIFS-192072_ref10","first-page":"33","article-title":"On some new calsses of sets and a new decomposition of continuity via grills","volume":"3","author":"Hatir","year":"2010","journal-title":"J Ads Math Studies"},{"key":"10.3233\/JIFS-192072_ref11","first-page":"1","article-title":"Graded fuzzy topological spaces","volume":"3","author":"Ibedou","year":"2016","journal-title":"Journal of Cogent Mathematics"},{"issue":"2","key":"10.3233\/JIFS-192072_ref12","doi-asserted-by":"crossref","first-page":"137","DOI":"10.30948\/afmi.2018.15.2.137","article-title":"Fuzzy topological concepts via ideals and grills","volume":"15","author":"Ibedou","year":"2018","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"key":"10.3233\/JIFS-192072_ref13","unstructured":"Kuratowski K. , Topology, Academic Press, New York, (1966)."},{"key":"10.3233\/JIFS-192072_ref14","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1080\/00029890.1990.11995593","article-title":"New topologies from old via ideals","volume":"97","author":"Jankovi\u0107","year":"1990","journal-title":"Amer Math Monthly"},{"issue":"6","key":"10.3233\/JIFS-192072_ref15","first-page":"453","article-title":"Compatible extensions of ideals","volume":"7","author":"Jankovi\u0107","year":"1992","journal-title":"Bollettino della Unione Matematica Italiana"},{"issue":"6","key":"10.3233\/JIFS-192072_ref16","first-page":"233","article-title":"On ideals and grills in topological spaces","volume":"5","author":"Kandil","year":"2015","journal-title":"South Asian Journal of Mathematics"},{"key":"10.3233\/JIFS-192072_ref17","doi-asserted-by":"crossref","first-page":"5919","DOI":"10.3233\/JIFS-181752","article-title":"Fuzzy ideal topological spaces","volume":"36","author":"Koam","year":"2019","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"13","key":"10.3233\/JIFS-192072_ref18","first-page":"107","article-title":"Nano-compactness and nano connectedness in Nano topological spaces","volume":"119","author":"Krishnaprakesh","year":"2018","journal-title":"Int J of Pure and Applied Mathematics"},{"key":"10.3233\/JIFS-192072_ref19","doi-asserted-by":"crossref","first-page":"1651","DOI":"10.1016\/j.ins.2007.11.010","article-title":"Generalized rough sets over fuzzy lattices","volume":"178","author":"Liu","year":"2008","journal-title":"Information Sciences"},{"issue":"1","key":"10.3233\/JIFS-192072_ref20","doi-asserted-by":"crossref","first-page":"443","DOI":"10.3233\/JIFS-152165","article-title":"Fuzzy soft topological spaces","volume":"32","author":"Mahanta","year":"2017","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-192072_ref21","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough Sets","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int J Inf Comput Sci"},{"issue":"4","key":"10.3233\/JIFS-192072_ref22","first-page":"771","article-title":"On a typical topology induced by a grill","volume":"33","author":"Roy","year":"2007","journal-title":"Soochow J Math"},{"key":"10.3233\/JIFS-192072_ref23","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/S0165-0114(96)00032-2","article-title":"Fuzzy ideal theory: Fuzzy local function and generated fuzzy topology","volume":"87","author":"Sarkar","year":"1997","journal-title":"Fuzzy Sets and Systems"},{"issue":"1","key":"10.3233\/JIFS-192072_ref24","first-page":"31","article-title":"On nano forms of weakly open sets","volume":"1","author":"Thivagar","year":"2013","journal-title":"International Journal of Mathematics and Statistics Invention"},{"key":"10.3233\/JIFS-192072_ref25","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1007\/BF03048958","article-title":"The localization theory in set topology","volume":"20","author":"Vaidyanathaswamy","year":"1945","journal-title":"Proc Indian Acad Sci"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-192072","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:41:16Z","timestamp":1777455676000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-192072"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,19]]},"references-count":24,"journal-issue":{"issue":"5"},"URL":"https:\/\/doi.org\/10.3233\/jifs-192072","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,19]]}}}