{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T05:08:20Z","timestamp":1764133700821,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T00:00:00Z","timestamp":1714003200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer the lattice structure of neutrosophic open sets of a neutrosophic topology generated via a neutrosophic relation and examine its different characteristics. Furthermore, we enlarge to this lattice structure the notions of ideals (respectively, filters) and characterize them with regard to the lattice operations. We end this work by studying the prime neutrosophic ideal and prime neutrosophic filter as interesting types of neutrosophic ideals and neutrosophic filters.<\/jats:p>","DOI":"10.3390\/axioms13050292","type":"journal-article","created":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T03:23:47Z","timestamp":1714101827000},"page":"292","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Ideals and Filters on Neutrosophic Topologies Generated by Neutrosophic Relations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0634-2370","authenticated-orcid":false,"given":"Ravi P.","family":"Agarwal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA"},{"name":"Department of Mathematics and Systems Engineering, Florida Institute of Technology, Melbourne, FL 32901, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8801-4607","authenticated-orcid":false,"given":"Soheyb","family":"Milles","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Institute of Science, University Center of Barika, Barika 05400, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Brahim","family":"Ziane","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matique et Physique Appliques, \u00c9cole Normale Sup\u00e9rieure de Bousaada, Bousaada 28200, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0791-5866","authenticated-orcid":false,"given":"Abdelaziz","family":"Mennouni","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Batna 2, Mostefa Ben Boula\u00efd, Fesdis, Batna 05078, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1420-9249","authenticated-orcid":false,"given":"Lemnaouar","family":"Zedam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Laboratory of Pure and Applied Mathematics, University of M\u2019sila, M\u2019sila 28000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,25]]},"reference":[{"key":"ref_1","unstructured":"Smarandache, F. (1998). Neutrosophy. Neutrosophic Property, Sets, and Logic, American Research Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/j.patcog.2008.10.002","article-title":"New neutrosophic approach to image segmentation","volume":"42","author":"Guo","year":"2009","journal-title":"Pattern Recognit."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/s00521-015-2048-z","article-title":"Multiple attribute decision making method based on some normal neutrosophic Bonferroni mean operators","volume":"28","author":"Liu","year":"2017","journal-title":"Neural Comput. Appl."},{"key":"ref_4","first-page":"21","article-title":"A study on problems of Hijras in West Bengal based on neutrosophic cognitive maps","volume":"5","author":"Mondal","year":"2014","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_5","first-page":"410","article-title":"Single valued neutrosophic sets","volume":"4","author":"Wang","year":"2010","journal-title":"Multispace Multistruct"},{"key":"ref_6","first-page":"385","article-title":"A unifying field in Logics: Neutrosophic Logic","volume":"8","author":"Smarandache","year":"2002","journal-title":"Mult.-Valued Log."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1108\/03684920810876990","article-title":"On neutrosophic topology","volume":"37","year":"2008","journal-title":"Kybernetes"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1016\/j.procs.2018.01.090","article-title":"On neutrosophic sets and topology","volume":"120","year":"2017","journal-title":"Procedia Comput. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"31","DOI":"10.9790\/5728-0343135","article-title":"Neutrosophic set and neutrosophic topological spaces","volume":"3","author":"Salama","year":"2012","journal-title":"IOSR J. Math."},{"key":"ref_10","first-page":"33","article-title":"Neutrosophic Relations Database","volume":"3","author":"Salama","year":"2014","journal-title":"Int. J. Inf. Sci. Intell. Syst."},{"key":"ref_11","first-page":"65","article-title":"Smooth Neutrosophic Topological Spaces","volume":"65","year":"2016","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3495","DOI":"10.2298\/FIL2010495G","article-title":"Neutrosophic Soft Continuity in Neutrosophic Soft Topological Spaces","volume":"34","author":"Bayramov","year":"2020","journal-title":"Filomat"},{"key":"ref_13","unstructured":"Kandil, A., Saleh, S., and Yakout, M.M. (2012). Fuzzy topology on fuzzy sets: Regularity and separation axioms. Am. Acad. Sch. Res. J., 4."},{"key":"ref_14","first-page":"203","article-title":"Single valued neutrosophic mappings defined by single valued neutrosophic relations with applications","volume":"32","author":"Latreche","year":"2020","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_15","first-page":"96","article-title":"Completeness and Compactness in Standard Single Valued Neutrosophic Metric Spaces","volume":"12","author":"Milles","year":"2020","journal-title":"Int. J. Neutrosophic Sci."},{"key":"ref_16","first-page":"942","article-title":"The Lattice of intuitionistic fuzzy topologies generated by intuitionistic fuzzy relations","volume":"15","author":"Milles","year":"2020","journal-title":"Appl. Appl. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1","DOI":"10.28924\/2291-8639-20-2022-48","article-title":"Fuzzy ideals and fuzzy filters on topologies generated by fuzzy relations","volume":"20","author":"Saadaoui","year":"2022","journal-title":"Int. J. Anal. Appl."},{"key":"ref_18","first-page":"175","article-title":"Several types of single-valued neutrosophic ideals and filters on a lattice","volume":"13","author":"Bennoui","year":"2023","journal-title":"TWMS J. App. Eng. Math."},{"key":"ref_19","first-page":"117","article-title":"Neutrosophic ideals in BCK\/BCI-algebras based on neutrosophic points","volume":"8","author":"Jun","year":"2018","journal-title":"J. Int. Math. Virtual Inst."},{"key":"ref_20","first-page":"34","article-title":"Fliters via neutrosophic crisp sets","volume":"1","author":"Salama","year":"2013","journal-title":"Neutrosophic Sets Syst."},{"key":"ref_21","first-page":"1140","article-title":"Ideals and filters on a lattice in neutrosophic setting","volume":"16","author":"Zedam","year":"2021","journal-title":"Appl. Appl. Math."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. Control"},{"key":"ref_23","unstructured":"Atanassov, K. (1983). Intuitionistic Fuzzy Sets, Sofia, VII ITKRs Scientific Session, Springer."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Atanassov, K. Intuitionistic Fuzzy Sets, Springer: New York, NY, USA; Berlin\/Heidelberg, Germany, 1999.","DOI":"10.1007\/978-3-7908-1870-3"},{"key":"ref_25","first-page":"225","article-title":"Fuzzy neutrosophic soft topological spaces","volume":"4","author":"Arockiarani","year":"2013","journal-title":"Int. J. Appl. Math. Arch."},{"key":"ref_26","unstructured":"Smarandache, F., and Pramanik, S. (2016). (Eds.) New Trends in Neutrosophic Theory and Applications, Pons Editions."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2453","DOI":"10.3233\/IFS-141215","article-title":"Improved correlation coefficients of single-valued neutrosophic sets and interval neutrosophic sets for multiple attribute decision making","volume":"27","author":"Ye","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_28","first-page":"2450","article-title":"Multicriteria decision-making method using aggregation operators for simplified neutrosophic sets","volume":"26","author":"Ye","year":"2014","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"81","DOI":"10.7151\/dmgaa.1345","article-title":"Representation and construction of intuitionistic fuzzy t-preorders and fuzzy weak t-orders","volume":"41","author":"Ziane","year":"2021","journal-title":"Discuss. Math. Gen. Algebra Appl."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"201","DOI":"10.30948\/afmi.2018.16.2.201","article-title":"Single valued neutrosophic relations","volume":"16","author":"Kim","year":"2018","journal-title":"Ann. Fuzzy Math. Inform."},{"key":"ref_31","unstructured":"Salama, A.A., and Smarandache, F. (2015). Neutrosophic Crisp Set Theory, The Educational Publisher."},{"key":"ref_32","first-page":"417","article-title":"Neutrosophic topologies generated by neutrosophic relations","volume":"5","author":"Milles","year":"2021","journal-title":"Alger. J. Eng. Archit. Urban."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1007\/s00500-016-2458-6","article-title":"Fuzzy topologies generated by fuzzy relations","volume":"22","author":"Mishra","year":"2018","journal-title":"Soft Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"165","DOI":"10.12732\/ijpam.v93i2.2","article-title":"Alexandrov L topologies","volume":"93","author":"Kim","year":"2014","journal-title":"Int. J. Pure Appl. Math."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/5\/292\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:33:06Z","timestamp":1760106786000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/5\/292"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,25]]},"references-count":34,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["axioms13050292"],"URL":"https:\/\/doi.org\/10.3390\/axioms13050292","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,4,25]]}}}