{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T02:22:21Z","timestamp":1775269341301,"version":"3.50.1"},"reference-count":19,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T00:00:00Z","timestamp":1753920000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Tanta University","award":["EGP2024-125635NB-I02"],"award-info":[{"award-number":["EGP2024-125635NB-I02"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We obtain different categories of singularities of fuzzy retracts, fuzzy deformation retracts, and fuzzy foldings on fuzzy fundamental groups of the fuzzy Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker Space W\u02dc4. The fuzzy fundamental groups of fuzzy submanifolds in W\u02dc4 are characterized combinatorially using these fuzzy geometrical transformations. Also, the fuzzy fundamental groups of the fuzzy geodesics and the limit fuzzy foldings of W\u02dc4 are described. New types of fuzzy singularity of some fuzzy geometrical transformations of W\u02dc4 are obtained. Finally, the regularity of some other fuzzy retract singularities are discussed.<\/jats:p>","DOI":"10.3390\/axioms14080591","type":"journal-article","created":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T08:46:55Z","timestamp":1754383615000},"page":"591","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Singularities of Fuzzy Friedmann\u2013Lema\u00eetre\u2013Robertson\u2013Walker Space"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1614-3228","authenticated-orcid":false,"given":"Yanlin","family":"Li","sequence":"first","affiliation":[{"name":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9786-8161","authenticated-orcid":false,"given":"Fawaz","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Umm Al-Qura University, Makkah 21955, Saudi Arabia"}]},{"given":"Abdulaziz E.","family":"El-Ahmady","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Tanta University, Tanta 31527, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,31]]},"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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