{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,1]],"date-time":"2026-02-01T19:22:10Z","timestamp":1769973730013,"version":"3.49.0"},"reference-count":50,"publisher":"SAGE Publications","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2023,7,2]]},"abstract":"<jats:p>A Q-neutrosophic soft environment is an innovative hybrid tool that combines features of both a Q-neutrosophic set (Q-NS) and a parametric tool \u201csoft set\u201d (SS) in order to manage imprecise and indeterminate situations in various mathematical problems. In this article, we introduce a new algebraic approach called Q-neutrosophic soft matrices (Q-NSMs) to address the issues of two-dimensional (two variables) in a universal set by representing the concept of Q-neutrosophic soft sets (Q-NSSs) in matrices. On Q-NSMs, we define the fundamental set operations and some algebraic operations, i.e., complement, union, intersection, addition, subtraction, multiplication, and scalar multiplication, and prove related properties of these operations. Moreover, these operations are illustrated via several numerical examples. Then, two algorithms are proposed to tackle group decision making (GDM) problems: The first depends on the score function of Q-NSMs, and the second is based on the aggregation operator of Q-NSMs. Finally, this study is supported by a brief comparison with some relevant previous models.<\/jats:p>","DOI":"10.3233\/jifs-224552","type":"journal-article","created":{"date-parts":[[2023,5,9]],"date-time":"2023-05-09T19:04:16Z","timestamp":1683659056000},"page":"305-321","source":"Crossref","is-referenced-by-count":7,"title":["Group decision-making based on aggregation operator and score function of Q-neutrosophic soft matrix"],"prefix":"10.1177","volume":"45","author":[{"given":"Faisal","family":"Al-Sharqi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq"}]},{"given":"Mamika Ujianita","family":"Romdhini","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, Mataram, Indonesia"}]},{"given":"Ashraf","family":"Al-Quran","sequence":"additional","affiliation":[{"name":"Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa, Saudi Arabia"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-224552_ref1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy set","volume":"8","author":"Zadeh","year":"1965","journal-title":"Information and Control"},{"issue":"1","key":"10.3233\/JIFS-224552_ref2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","article-title":"Intuitionistic fuzzy sets","volume":"20","author":"Atanassov","year":"1986","journal-title":"Fuzzy Sets and Systems"},{"key":"10.3233\/JIFS-224552_ref3","unstructured":"Smarandache F. , Neutrosophy: Neutrosophic probability, set and logic; American Research Press: Rehoboth, IL, USA, 1998."},{"key":"10.3233\/JIFS-224552_ref4","first-page":"287","article-title":"Neutrosophic set, a generalisation of the intuitionistic fuzzy sets","volume":"24","author":"Smarandache","year":"2005","journal-title":"International Journal of Pure and Applied Mathematics"},{"key":"10.3233\/JIFS-224552_ref5","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0898-1221(99)00056-5","article-title":"Soft set theory-first results","volume":"37","author":"Molodtsov","year":"1999","journal-title":"Computers &Mathematics with Applications"},{"key":"10.3233\/JIFS-224552_ref6","first-page":"157","article-title":"Neutrosophic soft set","volume":"5","author":"Maji","year":"2013","journal-title":"Ann. Fuzzy Math. Inform."},{"issue":"5","key":"10.3233\/JIFS-224552_ref7","doi-asserted-by":"crossref","first-page":"2417","DOI":"10.3233\/IFS-141211","article-title":"On similarity and entropy of neutrosophic soft sets","volume":"27","author":"Sahin","year":"2014","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"6","key":"10.3233\/JIFS-224552_ref8","doi-asserted-by":"crossref","first-page":"4087","DOI":"10.3233\/JIFS-17999","article-title":"Bipolar neutrosophic soft sets and applications in decision making","volume":"33","author":"Ali","year":"2017","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-224552_ref9","doi-asserted-by":"crossref","first-page":"32","DOI":"10.4018\/IJFSA.2018070103","article-title":"Application of bipolar intuitionistic fuzzy soft sets in decision-making problem","volume":"7","author":"Jana","year":"2018","journal-title":"International Journal of Fuzzy System Applications"},{"issue":"4","key":"10.3233\/JIFS-224552_ref10","doi-asserted-by":"crossref","first-page":"5531","DOI":"10.3233\/JIFS-190668","article-title":"A novel extension of TOPSIS to MCGDM with bipolar neutrosophic soft topology","volume":"37","author":"Tehrim","year":"2019","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"key":"10.3233\/JIFS-224552_ref11","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.asoc.2016.07.013","article-title":"Possibility neutrosophic soft sets and PNS-decision making method","volume":"54","author":"Karaaslan","year":"2017","journal-title":"Applied Soft Computing"},{"key":"10.3233\/JIFS-224552_ref12","first-page":"1","article-title":"The sequence of neutrosophic soft sets and a decision-making problem in medical diagnosis","author":"Bui","year":"2022","journal-title":"International Journal of Fuzzy Systems"},{"issue":"2","key":"10.3233\/JIFS-224552_ref13","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1007\/s13042-015-0461-3","article-title":"Interval-valued neutrosophic soft sets and its decision making","volume":"8","author":"Deli","year":"2017","journal-title":"International Journal of Machine Learning and Cybernetics"},{"issue":"1","key":"10.3233\/JIFS-224552_ref14","first-page":"11","article-title":"Similarity measure for m-polar interval valued neutrosophic soft set with application for medical diagnoses","volume":"47","author":"Zulqarnain","year":"2021","journal-title":"Neutrosophic Sets and Systems"},{"key":"10.3233\/JIFS-224552_ref15","doi-asserted-by":"crossref","first-page":"110","DOI":"10.3390\/sym11010110","article-title":"A robust single-valued neutrosophic soft aggregation operators in multi-criteria decision making","volume":"11","author":"Jana","year":"2019","journal-title":"Symmetry"},{"key":"10.3233\/JIFS-224552_ref16","first-page":"5055","article-title":"Multi-criteria decision-making process based on some single-valued neutrosophic Dombi power aggregation operators,\u2013","volume":"25","author":"Jana","year":"2021","journal-title":"Soft Computing"},{"issue":"1","key":"10.3233\/JIFS-224552_ref17","first-page":"149","article-title":"Interval-valued complex neutrosophic soft set and its applications in decision-making","volume":"40","author":"Al-Sharqi","year":"2021","journal-title":"Neutrosophic Sets and Systems"},{"issue":"1","key":"10.3233\/JIFS-224552_ref18","doi-asserted-by":"crossref","first-page":"267","DOI":"10.32604\/cmes.2022.019684","article-title":"Interval-valued neutrosophic soft expert set from real space to complex space","volume":"132","author":"Al-Sharqi","year":"2022","journal-title":"CMES-Computer Modeling in Engineering and Sciences"},{"issue":"1","key":"10.3233\/JIFS-224552_ref19","doi-asserted-by":"crossref","first-page":"745","DOI":"10.3233\/JIFS-212422","article-title":"Interval complex neutrosophic soft relations and their application in decision-making","volume":"43","author":"Al-Sharqi","year":"2022","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"1","key":"10.3233\/JIFS-224552_ref20","first-page":"495","article-title":"Similarity measures on interval-complex neutrosophic soft sets with applications to decision making and medical diagnosis under uncertainty","volume":"51","author":"Al-Sharqi","year":"2022","journal-title":"Neutrosophic Sets and Systems"},{"issue":"1","key":"10.3233\/JIFS-224552_ref21","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.3233\/JIFS-221579","article-title":"Fuzzy parameterized-interval complex neutrosophic soft sets and their applications under uncertainty","volume":"44","author":"Al-Sharqi","year":"2023","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"4","key":"10.3233\/JIFS-224552_ref22","doi-asserted-by":"crossref","first-page":"77","DOI":"10.54216\/IJNS.190406","article-title":"Mapping on interval complex neutrosophic soft sets","volume":"19","author":"Al-Sharqi","year":"2022","journal-title":"International Journal of Neutrosophic Science"},{"issue":"2","key":"10.3233\/JIFS-224552_ref23","doi-asserted-by":"crossref","first-page":"08","DOI":"10.54216\/IJNS.200201","article-title":"Q-complex neutrosophic set","volume":"20","author":"Al-Quran","year":"2023","journal-title":"International Journal of Neutrosophic Science"},{"issue":"2","key":"10.3233\/JIFS-224552_ref24","doi-asserted-by":"crossref","first-page":"139","DOI":"10.3390\/sym11020139","article-title":"An approach toward a Q-neutrosophic soft set and its application in decision making","volume":"11","author":"Qamar","year":"2019","journal-title":"Symmetry"},{"issue":"174","key":"10.3233\/JIFS-224552_ref25","first-page":"8689","article-title":"Q-fuzzy soft set","volume":"8","author":"Adam","year":"2019","journal-title":"Appl. Math. Sci"},{"key":"10.3233\/JIFS-224552_ref26","first-page":"81","article-title":"Q-intuitionistic fuzzy soft sets","volume":"5","author":"Broumi","year":"2015","journal-title":"Journal of New Theory"},{"key":"10.3233\/JIFS-224552_ref27","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.1007\/s10462-022-10207-3","article-title":"A novel perspective for Q-neutrosophic soft relations and their application in decision making","volume":"56","author":"Dalkl","year":"2023","journal-title":"Artificial Intelligence Review"},{"key":"10.3233\/JIFS-224552_ref28","first-page":"328","article-title":"The algebraic structure of normal groups associated with Q-neutrosophic soft sets","volume":"48","author":"Qamar","year":"2022","journal-title":"Neutrosophic Sets and Systems"},{"issue":"2","key":"10.3233\/JIFS-224552_ref29","first-page":"121","article-title":"Fuzzy soft matrix theory and its decision making","volume":"2","author":"Borah","year":"2012","journal-title":"International Journal of Modern Engineering Research"},{"issue":"1","key":"10.3233\/JIFS-224552_ref30","first-page":"109","article-title":"Fuzzy soft matrix theory and its decision making","volume":"9","author":"Cagman","year":"2012","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"10.3233\/JIFS-224552_ref31","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1007\/978-3-642-23881-9_79","article-title":"Fuzzy soft matrices and their applications","author":"Yang","year":"2011","journal-title":"In International Conference on Artificial Intelligence and Computational Intelligence"},{"issue":"1","key":"10.3233\/JIFS-224552_ref32","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1063\/1.4882573","article-title":"Q-fuzzy soft matrix and its application","volume":"1602","author":"Adam","year":"2014","journal-title":"In AIP Conference Proceedings"},{"issue":"1","key":"10.3233\/JIFS-224552_ref33","doi-asserted-by":"crossref","first-page":"4","DOI":"10.11648\/j.dmath.20200501.12","article-title":"Application of intuitionistic fuzzy soft matrices for disease diagnosis","volume":"5","author":"Zulqarnain","year":"2020","journal-title":"International Journal of Discrete Mathematics"},{"issue":"4","key":"10.3233\/JIFS-224552_ref34","first-page":"1","article-title":"Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application in decision-making","volume":"39","author":"Enginolu","year":"2020","journal-title":"Computational and Applied Mathematics"},{"issue":"5","key":"10.3233\/JIFS-224552_ref35","doi-asserted-by":"crossref","first-page":"2233","DOI":"10.3233\/IFS-141505","article-title":"Neutrosophic soft matrices and NSM-decision making","volume":"28","author":"Deli","year":"2015","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"1","key":"10.3233\/JIFS-224552_ref36","first-page":"2","article-title":"Neutrosophic soft matrix and its application to decision making","volume":"18","author":"Bera","year":"2017","journal-title":"Neutrosophic Sets and Systems"},{"issue":"4","key":"10.3233\/JIFS-224552_ref37","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.jksuci.2017.05.001","article-title":"Group decision making using neutrosophic soft matrix: An algorithmic approach","volume":"31","author":"Das","year":"2019","journal-title":"Journal of King Saud University-Computer and Information Sciences"},{"issue":"10","key":"10.3233\/JIFS-224552_ref38","doi-asserted-by":"crossref","first-page":"3308","DOI":"10.1016\/j.camwa.2010.03.015","article-title":"Soft matrix theory and its decision making","volume":"59","author":"Cagmanand","year":"2010","journal-title":"Computers and Mathematics with Applications"},{"issue":"1","key":"10.3233\/JIFS-224552_ref39","first-page":"168","article-title":"Extension of soft set to hypersoft set, and then to plithogenic hypersoft set","volume":"22","author":"Smarandache","year":"2018","journal-title":"Neutrosophic Sets and Systems"},{"issue":"1","key":"10.3233\/JIFS-224552_ref40","first-page":"12","article-title":"Hypersoft expert set with application in decision making for recruitment process","volume":"42","author":"Ihsan","year":"2021","journal-title":"Neutrosophic Sets and Systems"},{"issue":"1","key":"10.3233\/JIFS-224552_ref41","first-page":"12","article-title":"Decision-making approach based on correlation coefficient with its properties under interval-valued neutrosophic hypersoft set environment","volume":"40","author":"Zulqarnain","year":"2021","journal-title":"Neutrosophic Sets and Systems"},{"issue":"1","key":"10.3233\/JIFS-224552_ref42","doi-asserted-by":"crossref","first-page":"49","DOI":"10.37652\/juaps.2022.172431","article-title":"On Q-Injective, Duo Submodules of C1-Module","volume":"15","author":"Talak","year":"2021","journal-title":"Journal of University of Anbar for Pure Science"},{"issue":"18","key":"10.3233\/JIFS-224552_ref43","first-page":"7533","article-title":"On polish groups and their applications","volume":"13","author":"Al-Sharqi","year":"2018","journal-title":"Journal of Engineering and Applied Sciences"},{"issue":"1","key":"10.3233\/JIFS-224552_ref44","doi-asserted-by":"crossref","first-page":"54","DOI":"10.37652\/juaps.2022.172433","article-title":"Best multi approximation of unbounded functions by using modulus of smoothness","volume":"15","author":"Khashan","year":"2021","journal-title":"Journal of University of Anbar for Pure Science"},{"issue":"2","key":"10.3233\/JIFS-224552_ref45","first-page":"99","article-title":"Some mathematical structures in a topological group","volume":"16","author":"Abed","year":"2018","journal-title":"Journal of Algebra and Applied Mathematics"},{"issue":"1","key":"10.3233\/JIFS-224552_ref46","first-page":"1","article-title":"Sustainability strategy of agarwood-production trees in lombok island using harvesting matrix","volume":"1374","author":"Romdhini","year":"2019","journal-title":"Journal of Physics: Conference Series"},{"issue":"1","key":"10.3233\/JIFS-224552_ref47","first-page":"012101","article-title":"Other new types of mappings with strongly closed graphs in topological spaces via e-\u03b8 and \u03b4\u00a0-\u00a0\u03b2\u00a0-\u00a0\u03b8-open sets","volume":"1234","author":"Al-Jumaili","year":"2019","journal-title":"Journal of Physics: Conference Series"},{"issue":"3","key":"10.3233\/JIFS-224552_ref48","doi-asserted-by":"crossref","first-page":"3549","DOI":"10.3233\/JIFS-220707","article-title":"A new extension of fuzzy decision by opinion score method based on Fermatean fuzzy: A benchmarking COVID-19 machine learning methods","volume":"43","author":"Salih","year":"2022","journal-title":"Journal of Intelligent and Fuzzy Systems"},{"issue":"1","key":"10.3233\/JIFS-224552_ref49","first-page":"198","article-title":"On neutrosophic multiplication module","volume":"49","author":"Abed","year":"2022","journal-title":"Neutrosophic Sets and Systems"},{"issue":"12","key":"10.3233\/JIFS-224552_ref50","doi-asserted-by":"crossref","first-page":"4145","DOI":"10.17576\/jsm-2022-5112-21","article-title":"Maximum and minimum degree energy of commuting graph for dihedral groups","volume":"51","author":"Romdhini","year":"2022","journal-title":"Sains Malaysiana"}],"updated-by":[{"DOI":"10.1177\/10641246251331509","type":"retraction","label":"Retraction","source":"retraction-watch","updated":{"date-parts":[[2025,4,17]],"date-time":"2025-04-17T00:00:00Z","timestamp":1744848000000},"record-id":"64299"},{"DOI":"10.1177\/10641246251331509","type":"retraction","label":"Retraction","source":"publisher","updated":{"date-parts":[[2025,4,17]],"date-time":"2025-04-17T00:00:00Z","timestamp":1744848000000}}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-224552","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T07:46:52Z","timestamp":1769672812000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-224552"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7,2]]},"references-count":50,"journal-issue":{"issue":"1"},"URL":"https:\/\/doi.org\/10.3233\/jifs-224552","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7,2]]}}}