{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T12:24:47Z","timestamp":1777119887468,"version":"3.51.4"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T00:00:00Z","timestamp":1652227200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2022,5,11]]},"abstract":"<jats:p>In this paper, we introduce fuzzy nano (resp. \u03b4, \u03b4S, P and Z) locally closed set and fuzzy nano (resp. \u03b4, \u03b4S, P and Z) extremally disconnected spaces in fuzzy nano topological spaces. Also, we introduce some new spaces called fuzzy nano (resp. \u03b4, \u03b4S, P and Z) normal spaces and strongly fuzzy nano (resp. \u03b4, \u03b4S, P and Z) normal spaces with the help of fuzzy nano (resp. \u03b4, \u03b4S, P and Z)-open sets in fuzzy nano topological space. Numerical data is used to quantify the provided features. Furthermore, using fuzzy nano topological spaces, an algorithm for multiple attribute decision-making (MADM) with an application in medical diagnosis is devised.<\/jats:p>","DOI":"10.1155\/2022\/3364170","type":"journal-article","created":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T18:50:25Z","timestamp":1652295025000},"page":"1-9","source":"Crossref","is-referenced-by-count":7,"title":["Fuzzy Nano z-locally Closed Sets, Extremally Disconnected Spaces, Normal Spaces, and Their Application"],"prefix":"10.1155","volume":"2022","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2910-7445","authenticated-orcid":true,"given":"R.","family":"Thangammal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Selvamm College of Technology, Namakkal - 637 003, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3429-4591","authenticated-orcid":true,"given":"M.","family":"Saraswathi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kandaswami Kandar\u2019s College P-Velur, Tamil Nadu-638 182, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5970-035X","authenticated-orcid":true,"given":"A.","family":"Vadivel","sequence":"additional","affiliation":[{"name":"PG and Research Department of Mathematics, Government Arts College (Autonomous), India and Department of Mathematics, Annamalai University, Karur - 639 005, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2307-0891","authenticated-orcid":true,"given":"Samad","family":"Noeiaghdam","sequence":"additional","affiliation":[{"name":"Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, Irkutsk, 664074, Russia"},{"name":"Department of Applied Mathematics and Programming, South Ural State University, Lenin prospect 76, Chelyabinsk, 454080, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7455-4976","authenticated-orcid":true,"given":"C. John","family":"Sundar","sequence":"additional","affiliation":[{"name":"Department of Business Administration, Selvamm Arts and Science College (Autonomous), Namakkal-637 003, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4750-1964","authenticated-orcid":true,"given":"V.","family":"Govindan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Dmi St John The Baptist University, Mangochi, Malawi"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0475-3320","authenticated-orcid":true,"given":"Aiyared","family":"Iampan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/s0019-9958(65)90241-x"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.3390\/math8050850"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2019.112632"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.4018\/ijfsa.2017100101"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247x(68)90057-7"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-1461-5_1"},{"issue":"1","key":"7","first-page":"31","article-title":"On nano forms of weekly open sets","volume":"1","author":"M. Lellis Thivagar","year":"2013","journal-title":"Int. J. Math. Stat. Invention"},{"issue":"12","key":"8","first-page":"110","article-title":"-Open sets and -nano continuity in -nano topological spaces","volume":"2","author":"V. Pankajam","year":"2017","journal-title":"Int. J. Innovative Sci. Research Tech."},{"key":"9","first-page":"86","article-title":"A novel approach to nano topology via neutrosophic sets","volume":"20","author":"M. Lellis Thivagar","year":"2018","journal-title":"Neutrosophic Sets Syst"},{"issue":"10","key":"10","first-page":"1819","article-title":"Open sets and -continuity in topological spaces","volume":"2","author":"A. I. El-Magharabi","year":"2011","journal-title":"Int. J. Math. Archive"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.26637\/mjm0s01\/0117"},{"key":"12","article-title":"-Open sets in nano topological spaces","volume":"2364","author":"X. Arul Selvaraj","year":"2021","journal-title":"AIP Conference Proceedings"},{"key":"13","doi-asserted-by":"crossref","DOI":"10.1063\/5.0025765","article-title":"Fuzzy closed sets in double fuzzy topological spaces","volume":"2277","author":"S. Sathaananthan","year":"2020","journal-title":"AIP Conference Proceedings"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.37418\/amsj.9.4.70"},{"issue":"1","key":"15","first-page":"27","article-title":"Fuzzy nano -open sets in fuzzy nano topological spaces","volume":"11","author":"R. Thangammal","year":"2022","journal-title":"Journal of Linear and Topological Algebra"},{"key":"16","first-page":"22\u201425","article-title":"Surles differences de deux ensembles fermes","volume":"20","author":"C. Kuratowski","year":"1921","journal-title":"Tohoku Mathematical Journal"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1155\/s0161171289000505"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s40815-017-0368-0"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/2571301"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/5583218"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.3390\/sym13010069"}],"container-title":["Advances in Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2022\/3364170.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2022\/3364170.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2022\/3364170.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,11]],"date-time":"2022-05-11T18:50:39Z","timestamp":1652295039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/afs\/2022\/3364170\/"}},"subtitle":[],"editor":[{"given":"Antonin","family":"Dvor\u00e1k","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2022,5,11]]},"references-count":21,"alternative-id":["3364170","3364170"],"URL":"https:\/\/doi.org\/10.1155\/2022\/3364170","relation":{},"ISSN":["1687-711X","1687-7101"],"issn-type":[{"value":"1687-711X","type":"electronic"},{"value":"1687-7101","type":"print"}],"subject":[],"published":{"date-parts":[[2022,5,11]]}}}