{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T03:22:48Z","timestamp":1768447368207,"version":"3.49.0"},"reference-count":55,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,25]],"date-time":"2020-01-25T00:00:00Z","timestamp":1579910400000},"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>Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion of single-valued neutrosophic ideals sets in \u0160ostak\u2019s sense, which is considered as a generalization of fuzzy ideals in \u0160ostak\u2019s sense and intuitionistic fuzzy ideals. The concept of single-valued neutrosophic ideal open local function is also introduced for a single-valued neutrosophic topological space. The basic structure, especially a basis for such generated single-valued neutrosophic topologies and several relations between different single-valued neutrosophic ideals and single-valued neutrosophic topologies, are also studied here. Finally, for the purpose of symmetry, we also define the so-called single-valued neutrosophic relations.<\/jats:p>","DOI":"10.3390\/sym12020193","type":"journal-article","created":{"date-parts":[[2020,1,27]],"date-time":"2020-01-27T07:41:11Z","timestamp":1580110871000},"page":"193","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["On Single-Valued Neutrosophic Ideals in \u0160ostak Sense"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4795-3469","authenticated-orcid":false,"given":"Yaser","family":"Saber","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Human Studies, Hotat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science Al-Azhar University, Assiut 71524, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3818-3597","authenticated-orcid":false,"given":"Fahad","family":"Alsharari","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Human Studies, Hotat Sudair, Majmaah University, Majmaah 11952, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5560-5926","authenticated-orcid":false,"given":"Florentin","family":"Smarandache","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,25]]},"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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