{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T01:52:55Z","timestamp":1772934775810,"version":"3.50.1"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T00:00:00Z","timestamp":1772841600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T00:00:00Z","timestamp":1772841600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100010263","name":"Bingol University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100010263","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2026,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Hypersoft set theory has become an essential mathematical framework for modeling multi-parameter uncertainty; however, most of its current extensions, including fuzzy and intuitionistic hypersoft sets, still depend on the decision-maker\u2019s subjective evaluation when assigning (non-)membership degrees within the interval (0,\u00a01). This dependence restricts objectivity, reproducibility, and analytical robustness in uncertainty-based decision processes. To address this limitation, this paper introduces the novel concepts of relational and inverse relational hypersoft (non-)membership degrees, which enable the\n                    <jats:italic>objective computation<\/jats:italic>\n                    of these values through relational mappings that fully eliminate subjective numerical input. The proposed theoretical model is rigorously analyzed to ensure internal consistency, boundedness, and interpretability. Building on these concepts, two relational decision-making algorithms are developed to demonstrate their practical applicability. Experimental evaluation on an uncertainty problem reveals that the proposed relational hypersoft framework yields more reliable, consistent, and closer-to-ideal decisions compared to fuzzy-hypersoft and intuitionistic-hypersoft models. Moreover, the relational structure enhances information granularity and computational transparency by deriving (non-)membership degrees directly from binary expert judgments. Overall, this study contributes a mathematically grounded and decision-maker-independent approach that strengthens the theoretical foundation of hypersoft set theory and expands its practical capability in complex decision-making under uncertainty.\n                  <\/jats:p>","DOI":"10.1007\/s40314-026-03674-9","type":"journal-article","created":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T07:16:43Z","timestamp":1772867803000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Relational assessment in hypersoft sets: a decision-maker driven approach"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3875-1398","authenticated-orcid":false,"given":"Orhan","family":"Dalk\u0131l\u0131\u00e7","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,3,7]]},"reference":[{"key":"3674_CR1","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"K Atanassov","year":"1986","unstructured":"Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87\u201396","journal-title":"Fuzzy Sets Syst"},{"key":"3674_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-7908-1870-3","volume-title":"Intuitionistic Fuzzy Sets: Theory and Applications","author":"K Atanassov","year":"1999","unstructured":"Atanassov K (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg, Germany, pp 1\u2013137"},{"issue":"01","key":"3674_CR3","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1142\/S1793005721500113","volume":"17","author":"H Bordbar","year":"2021","unstructured":"Bordbar H, Khademan S, Borzooei RA, Zahedi MM, Jun YB (2021) Double-framed soft set theory applied to hyper BCK-algebras. New Math Natural Comput 17(01):215\u2013228","journal-title":"New Math Natural Comput"},{"key":"3674_CR4","doi-asserted-by":"publisher","first-page":"231","DOI":"10.22436\/jnsa.009.01.21","volume":"9","author":"V Cetkin","year":"2016","unstructured":"Cetkin V, Aygunoglu A, Aygun H (2016) A new approach in handling soft decision making problems. J Nonlin Sci App 9:231\u2013239","journal-title":"J Nonlin Sci App"},{"key":"3674_CR5","doi-asserted-by":"crossref","unstructured":"Dalk\u0131l\u0131\u00e7, O., Demirta\u015f, N. (2021) Bipolar fuzzy soft Dmetric spaces. Commun Facul Sci Univ Ankara Series A1 Math Stat, 70(1): 64\u201373","DOI":"10.31801\/cfsuasmas.774658"},{"issue":"1","key":"3674_CR6","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1080\/16583655.2021.1996800","volume":"15","author":"O Dalk\u0131l\u0131\u00e7","year":"2021","unstructured":"Dalk\u0131l\u0131\u00e7 O (2021) Determining the (non-)membership degrees in the range (0,1) independently of the decision-makers for bipolar soft sets. J Taibah Univ Sci 15(1):609\u2013618","journal-title":"J Taibah Univ Sci"},{"issue":"1","key":"3674_CR7","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/s12190-020-01495-5","volume":"67","author":"O Dalk\u0131l\u0131\u00e7","year":"2021","unstructured":"Dalk\u0131l\u0131\u00e7 O (2021) Relations on neutrosophic soft set and their application in decision making. J Appl Math Comput 67(1):257\u2013273","journal-title":"J Appl Math Comput"},{"issue":"10","key":"3674_CR8","doi-asserted-by":"publisher","first-page":"1935","DOI":"10.1080\/00207160.2020.1868445","volume":"98","author":"O Dalk\u0131l\u0131\u00e7","year":"2021","unstructured":"Dalk\u0131l\u0131\u00e7 O (2021) A novel approach to soft set theory in decision-making under uncertainty. Int J Comput Math 98(10):1935\u20131945","journal-title":"Int J Comput Math"},{"issue":"8","key":"3674_CR9","doi-asserted-by":"publisher","first-page":"1733","DOI":"10.1080\/00207721.2021.2023686","volume":"53","author":"O Dalk\u0131l\u0131\u00e7","year":"2022","unstructured":"Dalk\u0131l\u0131\u00e7 O (2022) Determining the membership degrees in the range (0, 1) for hypersoft sets independently of the decision-maker. Int J Syst Sci 53(8):1733\u20131743","journal-title":"Int J Syst Sci"},{"issue":"2","key":"3674_CR10","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1080\/00207721.2021.1949644","volume":"53","author":"O Dalk\u0131l\u0131\u00e7","year":"2022","unstructured":"Dalk\u0131l\u0131\u00e7 O (2022) A decision-making approach to reduce the margin of error of decision makers for bipolar soft set theory. Int J Syst Sci 53(2):265\u2013274","journal-title":"Int J Syst Sci"},{"issue":"2","key":"3674_CR11","first-page":"105","volume":"19","author":"O Dalk\u0131l\u0131\u00e7","year":"2022","unstructured":"Dalk\u0131l\u0131\u00e7 O (2022) Two novel approaches that reduce the effectiveness of the decision maker in decision making under uncertainty environments. Iranian J Fuzzy Syst 19(2):105\u2013117","journal-title":"Iranian J Fuzzy Syst"},{"issue":"2","key":"3674_CR12","first-page":"491","volume":"25","author":"O Dalk\u0131l\u0131\u00e7","year":"2022","unstructured":"Dalk\u0131l\u0131\u00e7 O (2022) An application of VFPFSS\u2019s in decision making problems. J Polytech 25(2):491\u2013501","journal-title":"J Polytech"},{"issue":"1","key":"3674_CR13","doi-asserted-by":"publisher","first-page":"21","DOI":"10.33773\/jum.679829","volume":"3","author":"O Dalk\u0131l\u0131\u00e7","year":"2020","unstructured":"Dalk\u0131l\u0131\u00e7 O, Demirta\u015f N (2020) Bipolar soft filter. J Univ Math 3(1):21\u201327","journal-title":"J Univ Math"},{"issue":"4","key":"3674_CR14","first-page":"1391","volume":"24","author":"O Dalk\u0131l\u0131\u00e7","year":"2021","unstructured":"Dalk\u0131l\u0131\u00e7 O, Demirta\u015f N (2021) VFP-soft k\u00fcmeler ve karar verme problemleri \u00fczerine uygulamas\u0131. J Polytech 24(4):1391\u20131399","journal-title":"J Polytech"},{"key":"3674_CR15","first-page":"86","volume":"31","author":"N Demirta\u015f","year":"2020","unstructured":"Demirta\u015f N, Dalk\u0131l\u0131\u00e7 O (2020) Decompositions of Soft $$\\alpha $$-continuity and Soft A-continuity. J New The 31:86\u201394","journal-title":"J New The"},{"issue":"3\u20134","key":"3674_CR16","first-page":"335","volume":"38","author":"N Demirta\u015f","year":"2020","unstructured":"Demirta\u015f N, Hussa\u0131n S, Dalk\u0131l\u0131\u00e7 O (2020) New approaches of inverse soft rough sets and their applications in a decision making problem. J Appl Math Info 38(3\u20134):335\u2013349","journal-title":"J Appl Math Info"},{"key":"3674_CR17","doi-asserted-by":"crossref","unstructured":"Fujita T (2025) Hyperfuzzy hypersoft set and hyperneutrosophic hypersoft set. Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond, 247","DOI":"10.31224\/4317"},{"key":"3674_CR18","first-page":"183","volume":"95","author":"T Fujita","year":"2026","unstructured":"Fujita T, Batiha IM (2026) Multiparameterized hypersoft set and type-2 hypersoft set. Neutrosophic Sets Syst 95:183\u2013199","journal-title":"Neutrosophic Sets Syst"},{"issue":"5","key":"3674_CR19","doi-asserted-by":"publisher","first-page":"2172","DOI":"10.19139\/soic-2310-5070-2599","volume":"14","author":"T Fujita","year":"2025","unstructured":"Fujita T, Hazaymeh AA, Batiha IM, Bataihah A, Oudetallah J (2025) Short Note of Linguistic SuperHypersoft Set. Stat Optimiz Info Comput 14(5):2172\u20132180","journal-title":"Stat Optimiz Info Comput"},{"issue":"8","key":"3674_CR20","doi-asserted-by":"publisher","first-page":"3337","DOI":"10.1007\/s00521-019-04291-w","volume":"32","author":"H Garg","year":"2020","unstructured":"Garg H, Kumar K (2020) A novel possibility measure to interval-valued intuitionistic fuzzy set using connection number of set pair analysis and its applications. Neural Comput Appl 32(8):3337\u20133348","journal-title":"Neural Comput Appl"},{"issue":"10","key":"3674_CR21","first-page":"114","volume":"16","author":"M Gilbert Rani","year":"2020","unstructured":"Gilbert Rani M, Muthulakshmi K (2020) Inverse hypersoft set theory. J Shanghai Jiaotong Univ (Chin Ed) 16(10):114\u2013120","journal-title":"J Shanghai Jiaotong Univ (Chin Ed)"},{"issue":"3","key":"3674_CR22","doi-asserted-by":"publisher","first-page":"2229","DOI":"10.1007\/s00500-019-04055-7","volume":"24","author":"K Hayat","year":"2020","unstructured":"Hayat K, Ali MI, Karaaslan F, Cao BY, Shah MH (2020) Design concept evaluation using soft sets based on acceptable and satisfactory levels: An integrated TOPSIS and Shannon entropy. Soft Comput 24(3):2229\u20132263","journal-title":"Soft Comput"},{"key":"3674_CR23","first-page":"191","volume":"42","author":"M Ihsan","year":"2021","unstructured":"Ihsan M, Rahman AU, Saeed M (2021) Hypersoft Expert Set With Application in Decision Making forRecruitment Process. Neutrosophic Sets Syst 42:191\u2013207","journal-title":"Neutrosophic Sets Syst"},{"issue":"3","key":"3674_CR24","first-page":"2031","volume":"34","author":"H Kamac\u0131","year":"2018","unstructured":"Kamac\u0131 H, Salt\u0131k K, Fulya Ak\u0131z H, Osman Atag\u00fcn A (2018) Cardinality inverse soft matrix theory and its applications in multicriteria group decision making. J Intell Fuzzy Syst 34(3):2031\u20132049","journal-title":"J Intell Fuzzy Syst"},{"issue":"1","key":"3674_CR25","first-page":"73","volume":"11","author":"AM Khalil","year":"2019","unstructured":"Khalil AM, Hassan N (2019) Inverse fuzzy soft set and its application in decision making. Int J Info Decis Sci 11(1):73\u201392","journal-title":"Int J Info Decis Sci"},{"issue":"1","key":"3674_CR26","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/s13198-019-00941-3","volume":"11","author":"PS Kumar","year":"2020","unstructured":"Kumar PS (2020) Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. Int J Syst Assur Eng Manag 11(1):189\u2013222","journal-title":"Int J Syst Assur Eng Manag"},{"key":"3674_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclepro.2020.122807","volume":"272","author":"AR Mishra","year":"2020","unstructured":"Mishra AR, Mardani A, Rani P, Zavadskas EK (2020) A novel EDAS approach on intuitionistic fuzzy set for assessment of health-care waste disposal technology using new parametric divergence measures. J Clean Prod 272:122807","journal-title":"J Clean Prod"},{"key":"3674_CR28","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0898-1221(99)00056-5","volume":"37","author":"D Molodtsov","year":"1999","unstructured":"Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37:19\u201331","journal-title":"Comput Math Appl"},{"key":"3674_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2019.105961","volume":"87","author":"RT Ngan","year":"2020","unstructured":"Ngan RT, Ali M, Tamir DE, Rishe ND, Kandel A (2020) Representing complex intuitionistic fuzzy set by quaternion numbers and applications to decision making. Appl Soft Comput 87:105961","journal-title":"Appl Soft Comput"},{"issue":"6","key":"3674_CR30","first-page":"6425","volume":"36","author":"S Petchimuthu","year":"2019","unstructured":"Petchimuthu S, Kamac\u0131 H (2019) The row-products of inverse soft matrices in multicriteria decision making. J Intell Fuzzy Syst 36(6):6425\u20136441","journal-title":"J Intell Fuzzy Syst"},{"key":"3674_CR31","unstructured":"Rahman AU, Saeed M, Smarandache F, Ahmad MR (2020) Development of hybrids of hypersoft set with complex fuzzy set, complex intuitionistic fuzzy set and complex neutrosophic set. 38(1), 335\u2013354"},{"key":"3674_CR32","first-page":"1","volume":"41","author":"AU Rahman","year":"2021","unstructured":"Rahman AU, Saeed M, Dhital A (2021) Decision making application based on neutrosophic parameterized hypersoft set theory. Neutrosophic Sets Syst 41:1\u201314","journal-title":"Neutrosophic Sets Syst"},{"key":"3674_CR33","doi-asserted-by":"crossref","unstructured":"Riaz, M., Shahzadi, T., Saqlain, M., Merigo, J. M. (2025). Integrated LOPCOW-AROMAN framework with softmax hamacher information aggregation: Enhancing airport security screening efficiency in uncertain environment. Information Sciences, 122776","DOI":"10.1016\/j.ins.2025.122776"},{"key":"3674_CR34","first-page":"2229","volume":"11","author":"M Saeed","year":"2020","unstructured":"Saeed M, Ahsan M, Siddique MK, Ahmad MR (2020) A study of the fundamentals of hypersoft set theory. Int J Sci Eng Res 11:2229\u20135518","journal-title":"Int J Sci Eng Res"},{"key":"3674_CR35","doi-asserted-by":"publisher","first-page":"60026","DOI":"10.1109\/ACCESS.2021.3073206","volume":"9","author":"M Saeed","year":"2021","unstructured":"Saeed M, Ahsan M, Abdeljawad T (2021) A development of complex multi-fuzzy hypersoft set with application in MCDM based on entropy and similarity measure. IEEE Access 9:60026\u201360042","journal-title":"IEEE Access"},{"key":"3674_CR36","first-page":"317","volume":"32","author":"M Saqlain","year":"2020","unstructured":"Saqlain M, Jafar N, Moin S, Saeed M, Broumi S (2020) Single and multi-valued neutrosophic hypersoft set and tangent similarity measure of single valued neutrosophic hypersoft sets. Neutrosophic Sets Syst 32:317\u2013329","journal-title":"Neutrosophic Sets Syst"},{"key":"3674_CR37","first-page":"294","volume":"32","author":"M Saqlain","year":"2020","unstructured":"Saqlain M, Moin S, Jafar MN, Saeed M, Smarandache F (2020) Aggregate operators of neutrosophic hypersoft set. Neutrosophic Sets Syst 32:294\u2013306","journal-title":"Neutrosophic Sets Syst"},{"key":"3674_CR38","doi-asserted-by":"crossref","unstructured":"Saqlain, M., Merigo, J. M., Kumam, P., Pamucar, D. (2025). OWA operators and probabilities under hypersoft set environments. Systems and Soft Computing, 200408","DOI":"10.1016\/j.sasc.2025.200408"},{"issue":"2","key":"3674_CR39","first-page":"344","volume":"6","author":"M Saqlain","year":"2025","unstructured":"Saqlain M, Kumam P, Kumam W (2025) Multi-criteria decision-making method based on weighted and geometric aggregate operators of linguistic fuzzy-valued hypersoft set with application. J Fuzzy Ext Appl 6(2):344\u2013370","journal-title":"J Fuzzy Ext Appl"},{"key":"3674_CR40","doi-asserted-by":"crossref","unstructured":"Saqlain M, Merigo JM, Kumam P, Pamucar D (2025) OWA operators and probabilities under hypersoft set environments. Systems and Soft Computing, 200408","DOI":"10.1016\/j.sasc.2025.200408"},{"issue":"5","key":"3674_CR41","doi-asserted-by":"publisher","first-page":"3417","DOI":"10.1007\/s00500-021-05610-x","volume":"25","author":"M Sarwar","year":"2021","unstructured":"Sarwar M, Akram M, Shahzadi S (2021) Bipolar fuzzy soft information applied to hypergraphs. Soft Comput 25(5):3417\u20133439","journal-title":"Soft Comput"},{"key":"3674_CR42","first-page":"168","volume":"22","author":"F Smarandache","year":"2018","unstructured":"Smarandache F (2018) Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic Sets Syst 22:168\u2013170","journal-title":"Neutrosophic Sets Syst"},{"issue":"1","key":"3674_CR43","doi-asserted-by":"publisher","first-page":"15","DOI":"10.30948\/afmi.2019.18.1.15","volume":"18","author":"P Suebsan","year":"2019","unstructured":"Suebsan P (2019) Inverse int-fuzzy soft bi-ideals over semigroups. Ann Fuzzy Math Inform 18(1):15\u201330","journal-title":"Ann Fuzzy Math Inform"},{"issue":"1","key":"3674_CR44","doi-asserted-by":"publisher","first-page":"5770","DOI":"10.1038\/s41598-024-56252-6","volume":"14","author":"AN Surya","year":"2024","unstructured":"Surya AN, Vimala J, Kausar N, Stevi\u0107 \u017d, Shah MA (2024) Entropy for q-rung linear diophantine fuzzy hypersoft set with its application in MADM. Sci Rep 14(1):5770","journal-title":"Sci Rep"},{"issue":"2","key":"3674_CR45","first-page":"1283","volume":"17","author":"AN Surya","year":"2025","unstructured":"Surya AN, Vimala J, Vizhi MT (2025) Bonferroni mean aggregation operators under q-rung linear diophantine fuzzy hypersoft set environment and its application in multi-attribute decision making. Int J Inf Technol 17(2):1283\u20131306","journal-title":"Int J Inf Technol"},{"key":"3674_CR46","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Info Control 8:338\u2013353","journal-title":"Info Control"},{"key":"3674_CR47","doi-asserted-by":"publisher","DOI":"10.5281\/zenodo.4788064","author":"RM Zulqarnain","year":"2021","unstructured":"Zulqarnain RM, Xin XL, Saeed M (2021) A Development of Pythagorean fuzzy hypersoft set with basic operations and decision-making approach based on the correlation coefficient. Theory App Hypersoft Set. https:\/\/doi.org\/10.5281\/zenodo.4788064","journal-title":"Theory App Hypersoft Set"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-026-03674-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-026-03674-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-026-03674-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T07:16:48Z","timestamp":1772867808000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-026-03674-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,7]]},"references-count":47,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2026,8]]}},"alternative-id":["3674"],"URL":"https:\/\/doi.org\/10.1007\/s40314-026-03674-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,7]]},"assertion":[{"value":"6 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 January 2026","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 January 2026","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 March 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The author declares that he has no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Informed consent was obtained from all individual participants included in the study, including their legal guardians.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical and informed consent for data used"}}],"article-number":"288"}}