{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:40:46Z","timestamp":1776397246713,"version":"3.51.2"},"reference-count":22,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T00:00:00Z","timestamp":1766707200000},"content-version":"vor","delay-in-days":359,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>In this paper, we introduce the novel structure of the \u2010rung orthopair neutrosophic metric space (\u2010), which unifies and extends the frameworks of \u2010rung orthopair fuzzy sets and neutrosophic metric spaces. The proposed model incorporates membership, nonmembership, and indeterminacy degrees within a \u2010rung orthopair framework, thereby offering a more flexible and expressive structure to capture uncertainty, inconsistency, and indeterminacy in data. Fundamental topological properties of the space are rigorously developed, including notions of open balls, induced topology, compactness, completeness, convergence, and Hausdorffness. Several illustrative examples are provided to support theoretical developments. Furthermore, the relevance of the proposed structure is highlighted through applications in decision\u2010making under uncertainty, artificial intelligence, multicriteria decision\u2010making (MCDM), image processing, and clustering. This framework lays the foundation for further exploration in modeling real\u2010world problems involving complex, vague, and imprecise information.<\/jats:p>","DOI":"10.1155\/jama\/1554812","type":"journal-article","created":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T11:29:10Z","timestamp":1766748550000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On q`\u2010Rung Orthopair Neutrosophic Metric Spaces and Topological Properties"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-3970-0987","authenticated-orcid":false,"given":"N.","family":"Muthulakshmi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9111-7129","authenticated-orcid":false,"given":"D.","family":"Poovaragavan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0364-1845","authenticated-orcid":false,"given":"M.","family":"Jeyaraman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9835-0935","authenticated-orcid":false,"given":"Rahul","family":"Shukla","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,12,26]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00244-9"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(86)90077-1"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)90162-7"},{"key":"e_1_2_9_6_2","first-page":"336","article-title":"Fuzzy Metric and Statistical Metric Spaces","volume":"23","author":"Kramosil I.","year":"1987","journal-title":"Kybernetika"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.02.051"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym14071400"},{"key":"e_1_2_9_9_2","volume-title":"Neutrosophy: Neutrosophic Probability, Set, and Logic: Analytic Synthesis & Synthetic Analysis","author":"Smarandache F.","year":"1998"},{"key":"e_1_2_9_10_2","volume-title":"Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability","author":"Smarandache F.","year":"2014"},{"key":"e_1_2_9_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40096-020-00335-8"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym16111446"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym16050613"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.3390\/fractalfract6060318"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.28924\/2291-8639-23-2025-96"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2022811"},{"key":"e_1_2_9_17_2","first-page":"308","article-title":"Fixed Point Results for Contraction Theorems in Neutrosophic Metric Spaces","volume":"36","author":"Sowndrarajan S.","year":"2020","journal-title":"Neutrosophic Sets and Systems"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2022477"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.61356\/j.nswa.2024.1515356"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2016.2604005"},{"key":"e_1_2_9_21_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.22028"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-16-1989-2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/1554812","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/1554812","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/1554812","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:41:48Z","timestamp":1776393708000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/1554812"}},"subtitle":[],"editor":[{"given":"AbdelMaksoud","family":"Soliman","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/1554812"],"URL":"https:\/\/doi.org\/10.1155\/jama\/1554812","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2025-04-23","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-10-17","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-12-26","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"1554812"}}