{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:28:44Z","timestamp":1763468924432,"version":"3.41.0"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:p> The premise of the soft set was designed to model vague ideas. In this kind of model, where the set of parameters exhibits some degree of order, lattice order theory is quite beneficial. For researchers studying uncertainty, the notion of soft sets, lattices, and fuzzy sets has proven essential. In this study, the postulation of the Lattice ordered Linear Diophantine Multi-Fuzzy Soft Set (LLDMFSS) is laid out. The fundamental objective of this study is the formation of hybrid algebraic structures for LLDMFSS. Particularly, the characteristics of complete lattice, modular lattice, and distributive lattice were inhibited in LLDMFSS, and some pertinent findings were obtained. Subsequently, the modular and distributive LLDMFSS characterization theorem was implemented. The notion of the direct product for two LLDMFSSs was then addressed. <\/jats:p>","DOI":"10.1142\/s1793005725500218","type":"journal-article","created":{"date-parts":[[2024,2,25]],"date-time":"2024-02-25T02:58:26Z","timestamp":1708829906000},"page":"487-507","source":"Crossref","is-referenced-by-count":4,"title":["Lattice Algebraic Structures on LDMFS Domains"],"prefix":"10.1142","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7846-9173","authenticated-orcid":false,"given":"Jeevitha","family":"Kannan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Alagappa University, Karaikudi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3138-9365","authenticated-orcid":false,"given":"Vimala","family":"Jayakumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Alagappa University, Karaikudi, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9495-6027","authenticated-orcid":false,"given":"Arsham Borumand","family":"Saeid","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2024,3,21]]},"reference":[{"key":"S1793005725500218BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"S1793005725500218BIB002","doi-asserted-by":"publisher","DOI":"10.3390\/sym13060945"},{"key":"S1793005725500218BIB003","doi-asserted-by":"publisher","DOI":"10.1080\/09720529.2019.1685239"},{"volume-title":"Lattice Theory","year":"1967","author":"Birkhoff G.","key":"S1793005725500218BIB004"},{"key":"S1793005725500218BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0018-1"},{"key":"S1793005725500218BIB006","doi-asserted-by":"publisher","DOI":"10.3390\/axioms10030185"},{"key":"S1793005725500218BIB007","first-page":"2225","volume":"3","author":"Karaaslan F.","year":"2013","journal-title":"ARPN Journal of Science and Technology"},{"key":"S1793005725500218BIB008","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2023.3239675"},{"key":"S1793005725500218BIB009","doi-asserted-by":"publisher","DOI":"10.31801\/cfsuasmas.1255830"},{"issue":"2","key":"S1793005725500218BIB010","first-page":"3097","volume":"45","author":"Jeevitha K.","year":"2023","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"S1793005725500218BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s00477-023-02618-7"},{"key":"S1793005725500218BIB012","doi-asserted-by":"publisher","DOI":"10.20454\/ijas.2018.1434"},{"issue":"3","key":"S1793005725500218BIB013","first-page":"235","volume":"4","author":"Mahalakshmi P.","year":"2023","journal-title":"Journal of Fuzzy Extension and Applications"},{"key":"S1793005725500218BIB014","first-page":"589","volume":"3","author":"Maji P. K.","year":"2001","journal-title":"Journal of Fuzzy Mathematics"},{"key":"S1793005725500218BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(99)00056-5"},{"key":"S1793005725500218BIB016","first-page":"6019","volume":"2","author":"Nagarajan E. K. R.","year":"2013","journal-title":"International Journal of Innovative Research in Science, Engineering and Technology"},{"issue":"2","key":"S1793005725500218BIB017","first-page":"517","author":"Natarajan R.","year":"2007","journal-title":"Acta Ciencia Indica"},{"key":"S1793005725500218BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/s11766-016-3411-2"},{"key":"S1793005725500218BIB019","first-page":"5417","volume":"37","author":"Riaz M.","year":"2019","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"S1793005725500218BIB020","doi-asserted-by":"publisher","DOI":"10.3390\/sym12081215"},{"key":"S1793005725500218BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s12543-011-0064-y"},{"issue":"4","key":"S1793005725500218BIB022","first-page":"44","volume":"26","author":"Vimala J.","year":"2023","journal-title":"International Journal of Fuzzy Systems"},{"key":"S1793005725500218BIB023","doi-asserted-by":"publisher","DOI":"10.47852\/bonviewJCCE2202193"},{"key":"S1793005725500218BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-023-08976-2"},{"key":"S1793005725500218BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.10.015"},{"key":"S1793005725500218BIB026","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2013.2278989"},{"key":"S1793005725500218BIB027","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2016.2604005"},{"key":"S1793005725500218BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"}],"container-title":["New Mathematics and Natural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793005725500218","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T07:09:55Z","timestamp":1750662595000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793005725500218"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,21]]},"references-count":28,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2025,7]]}},"alternative-id":["10.1142\/S1793005725500218"],"URL":"https:\/\/doi.org\/10.1142\/s1793005725500218","relation":{},"ISSN":["1793-0057","1793-7027"],"issn-type":[{"type":"print","value":"1793-0057"},{"type":"electronic","value":"1793-7027"}],"subject":[],"published":{"date-parts":[[2024,3,21]]}}}