{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T17:17:00Z","timestamp":1772990220658,"version":"3.50.1"},"reference-count":34,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T00:00:00Z","timestamp":1753747200000},"content-version":"vor","delay-in-days":209,"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":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2025,1]]},"abstract":"\n The notion of parameter mappings is about creating and managing a structured relationship between parameters across different systems or processes. This concept is vital in ensuring that data remains consistent, correctly interpreted, and accurately transformed as it moves through different parts of a system or between different systems. In this paper, the concept of reference parameter mappings is introduced to handle reference parameters that will help the decision makers. To overcome the uncertainty by giving direct value to reference parameters without any rule, a new class of fuzzy sets is presented which is known as (\n q<\/jats:italic>\n 1<\/jats:sub>\n ,\n q<\/jats:italic>\n 2<\/jats:sub>\n )\u2010linear Diophantine fuzzy set ((\n q<\/jats:italic>\n 1<\/jats:sub>\n ,\n q<\/jats:italic>\n 2<\/jats:sub>\n )\n L<\/jats:italic>\n D<\/jats:italic>\n F<\/jats:italic>\n S<\/jats:italic>\n ), where\n q<\/jats:italic>\n 1<\/jats:sub>\n and\n q<\/jats:italic>\n 2<\/jats:sub>\n are reference parameter mappings. Because the\n q<\/jats:italic>\n 1<\/jats:sub>\n and\n q<\/jats:italic>\n 2<\/jats:sub>\n can reflect a wider variety of reference parameters than LDFSs and\n q<\/jats:italic>\n \u2010rung LDFSs, (\n q<\/jats:italic>\n 1<\/jats:sub>\n ,\n q<\/jats:italic>\n 2<\/jats:sub>\n )\n L<\/jats:italic>\n D<\/jats:italic>\n F<\/jats:italic>\n S<\/jats:italic>\n s<\/jats:italic>\n can provide more ambiguous conditions. There is symmetry in the values of both the membership grades function and the nonmembership grades function. Furthermore, when discussing the symmetry between two or more objects, the evolution of a ((\n q<\/jats:italic>\n 1<\/jats:sub>\n ,\n q<\/jats:italic>\n 2<\/jats:sub>\n )\n L<\/jats:italic>\n D<\/jats:italic>\n F<\/jats:italic>\n S<\/jats:italic>\n s<\/jats:italic>\n via\n q<\/jats:italic>\n 1<\/jats:sub>\n and\n q<\/jats:italic>\n 2<\/jats:sub>\n is more adaptable than the diffused concept of a\n q<\/jats:italic>\n \u2010rung orthopair fuzzy sets or a LDFSs. The primary benefit of (\n q<\/jats:italic>\n 1<\/jats:sub>\n ,\n q<\/jats:italic>\n 2<\/jats:sub>\n )\n L<\/jats:italic>\n D<\/jats:italic>\n F<\/jats:italic>\n S<\/jats:italic>\n s<\/jats:italic>\n , which are useful in a variety of decision\u2010making situations, is that they are able to characterize a greater number of uncertainties with respect to reference parameter mappings\n q<\/jats:italic>\n 1<\/jats:sub>\n and\n q<\/jats:italic>\n 2<\/jats:sub>\n than LDFSs. Next, we propose several geometric and averaging operators for a (\n q<\/jats:italic>\n 1<\/jats:sub>\n ,\n q<\/jats:italic>\n 2<\/jats:sub>\n ) linear Diophantine fuzzy numbers, based on established operating rules. In the latter half of the paper, different ranking algorithms based on proposed aggregation operators are presented to address a realistic assessment of the patient\u2019s high blood pressure conditions is conducted to demonstrate the viability and value of the suggested strategies.\n <\/jats:p>","DOI":"10.1155\/ijmm\/9965947","type":"journal-article","created":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T18:53:27Z","timestamp":1753815207000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Introduction to (\n q<\/i>\n 1<\/sub>\n ,\n q<\/i>\n 2<\/sub>\n )\u2010Linear Diophantine Fuzzy Sets and Their Applications"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7450-8067","authenticated-orcid":false,"given":"Muhammad Bilal","family":"Khan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1070-1383","authenticated-orcid":false,"given":"Adrian Marius","family":"Deaconu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7559-3870","authenticated-orcid":false,"given":"Javad","family":"Tayyebi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2160-4159","authenticated-orcid":false,"given":"Bandar","family":"Bin-Mohsin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1234-7939","authenticated-orcid":false,"given":"Loredana","family":"Ciurdariu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1567-0264","authenticated-orcid":false,"given":"Miguel Vivas","family":"Cortez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2039-6682","authenticated-orcid":false,"given":"Nurnadiah","family":"Zamri","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,7,29]]},"reference":[{"key":"e_1_2_12_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0019-9958(65)90241-x"},{"key":"e_1_2_12_2_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2023095"},{"key":"e_1_2_12_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2022.3169862"},{"key":"e_1_2_12_4_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/4168124"},{"key":"e_1_2_12_5_2","first-page":"338","article-title":"Linear Diophantine Fuzzy Sets over Complex Fuzzy Information with Applications in Information Theory","volume":"8","author":"Yousafzai F.","year":"2023","journal-title":"Ain Shams Engineering Journal"},{"key":"e_1_2_12_6_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2023618"},{"key":"e_1_2_12_7_2","doi-asserted-by":"publisher","DOI":"10.3233\/jifs-190550"},{"key":"e_1_2_12_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0165-0114(86)80034-3"},{"key":"e_1_2_12_9_2","doi-asserted-by":"publisher","DOI":"10.1155\/2022\/3136462"},{"key":"e_1_2_12_10_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2022627"},{"key":"e_1_2_12_11_2","doi-asserted-by":"publisher","DOI":"10.3390\/axioms10030185"},{"key":"e_1_2_12_12_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym13091616"},{"key":"e_1_2_12_13_2","doi-asserted-by":"publisher","DOI":"10.3390\/sym13060945"},{"key":"e_1_2_12_14_2","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/5548033"},{"key":"e_1_2_12_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12652-020-02826-x"},{"key":"e_1_2_12_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-022-02077-w"},{"key":"e_1_2_12_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-021-00573-w"},{"key":"e_1_2_12_18_2","doi-asserted-by":"publisher","DOI":"10.15330\/cmp.14.2.564-581"},{"key":"e_1_2_12_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/tfuzz.2013.2278989"},{"key":"e_1_2_12_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/tfuzz.2016.2604005"},{"key":"e_1_2_12_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2022.3151684"},{"key":"e_1_2_12_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40747-022-00653-5"},{"key":"e_1_2_12_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12652-021-03130-y"},{"key":"e_1_2_12_24_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2023337"},{"key":"e_1_2_12_25_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2023497"},{"key":"e_1_2_12_26_2","doi-asserted-by":"publisher","DOI":"10.1007\/s40314-023-02456-x"},{"key":"e_1_2_12_27_2","doi-asserted-by":"publisher","DOI":"10.31181\/sor2120258"},{"key":"e_1_2_12_28_2","doi-asserted-by":"publisher","DOI":"10.22190\/fume230805029w"},{"key":"e_1_2_12_29_2","doi-asserted-by":"publisher","DOI":"10.31181\/smeor11202421"},{"key":"e_1_2_12_30_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.20097"},{"key":"e_1_2_12_31_2","doi-asserted-by":"publisher","DOI":"10.47852\/bonviewjcce3202420"},{"key":"e_1_2_12_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2006.02.086"},{"key":"e_1_2_12_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/s44196-021-00009-w"},{"key":"e_1_2_12_34_2","doi-asserted-by":"publisher","DOI":"10.1109\/access.2022.3207184"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/ijmm\/9965947","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/ijmm\/9965947","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/ijmm\/9965947","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T12:17:27Z","timestamp":1772972247000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/ijmm\/9965947"}},"subtitle":[],"editor":[{"given":"Nadeem ur","family":"Rehman","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":34,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/ijmm\/9965947"],"URL":"https:\/\/doi.org\/10.1155\/ijmm\/9965947","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-12-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-03-27","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-07-29","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"9965947"}}