{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T08:57:12Z","timestamp":1775120232315,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T00:00:00Z","timestamp":1731974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62466017"],"award-info":[{"award-number":["62466017"]}]},{"name":"National Natural Science Foundation of China","award":["62066014"],"award-info":[{"award-number":["62066014"]}]},{"name":"National Natural Science Foundation of China","award":["62163016"],"award-info":[{"award-number":["62163016"]}]},{"name":"National Natural Science Foundation of China","award":["20232ACB202013"],"award-info":[{"award-number":["20232ACB202013"]}]},{"name":"Double thousand plan of Jiangxi Province of China, the Natural Science Foundation of Jiangxi Province","award":["62466017"],"award-info":[{"award-number":["62466017"]}]},{"name":"Double thousand plan of Jiangxi Province of China, the Natural Science Foundation of Jiangxi Province","award":["62066014"],"award-info":[{"award-number":["62066014"]}]},{"name":"Double thousand plan of Jiangxi Province of China, the Natural Science Foundation of Jiangxi Province","award":["62163016"],"award-info":[{"award-number":["62163016"]}]},{"name":"Double thousand plan of Jiangxi Province of China, the Natural Science Foundation of Jiangxi Province","award":["20232ACB202013"],"award-info":[{"award-number":["20232ACB202013"]}]},{"name":"National Natural Science Foundation of China","award":["62466017"],"award-info":[{"award-number":["62466017"]}]},{"name":"National Natural Science Foundation of China","award":["62066014"],"award-info":[{"award-number":["62066014"]}]},{"name":"National Natural Science Foundation of China","award":["62163016"],"award-info":[{"award-number":["62163016"]}]},{"name":"National Natural Science Foundation of China","award":["20232ACB202013"],"award-info":[{"award-number":["20232ACB202013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>VIKOR uses the idea of overall utility maximization and individual regret minimization to afford a compromise result for multi-attribute decision-making problems with conflicting attributes. Many researchers have proposed corresponding improvements and expansions to make it more suitable for sorting optimization in their respective research fields. However, these improvements and extensions only rank the alternatives without classifying them. For this purpose, this text introduces the three-way sequential decisions method and combines it with the VIKOR method to design a three-way VIKOR method that can deal with both ranking and classification. By using the final negative ideal solution (NIS) and the final positive ideal solution (PIS) for all alternatives, the individual regret value and group utility value of each alternative were calculated. Different three-way VIKOR models were obtained by four different combinations of individual regret value and group utility value. In the ranking process, the characteristics of VIKOR method are introduced, and the subjective preference of decision makers is considered by using individual regret, group utility, and decision index values. In the classification process, the corresponding alternatives are divided into the corresponding decision domains by sequential three-way decisions, and the risk of direct acceptance or rejection is avoided by putting the uncertain alternatives into the boundary region to delay the decision. The alternative is divided into decision domains through sequential three-way decisions, sorted according to the collation rules in the same decision domain, and the final sorting results are obtained according to the collation rules in different decision domains. Finally, the effectiveness and correctness of the proposed method are verified by a project investment example, and the results are compared and evaluated. The experimental results show that the proposed method has a significant correlation with the results of other methods, ad is effective and feasible, and is simpler and more effective in dealing with some problems. Errors caused by misclassification is reduced by sequential three-way decisions.<\/jats:p>","DOI":"10.3390\/a17110530","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T07:51:15Z","timestamp":1732002675000},"page":"530","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A VIKOR-Based Sequential Three-Way Classification Ranking Method"],"prefix":"10.3390","volume":"17","author":[{"given":"Wentao","family":"Xu","sequence":"first","affiliation":[{"name":"School of Information and Software Engineering, East China JiaoTong University, Nanchang 330000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jin","family":"Qian","sequence":"additional","affiliation":[{"name":"School of Information and Software Engineering, East China JiaoTong University, Nanchang 330000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yueyang","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information and Software Engineering, East China JiaoTong University, Nanchang 330000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaowei","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Information and Software Engineering, East China JiaoTong University, Nanchang 330000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongting","family":"Ni","sequence":"additional","affiliation":[{"name":"School of Information and Software Engineering, East China JiaoTong University, Nanchang 330000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guangjin","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer, Jiangsu University of Science and Technology, Zhenjiang 212000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111055","DOI":"10.1016\/j.knosys.2023.111055","article-title":"An improvement to the interval type-2 fuzzy VIKOR method","volume":"280","author":"Jana","year":"2023","journal-title":"Knowl.-Based Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"123386","DOI":"10.1016\/j.eswa.2024.123386","article-title":"A FAHP-VIKOR model for evaluating single point interchange operational performance","volume":"248","author":"Alhadidi","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"106857","DOI":"10.1016\/j.engappai.2023.106857","article-title":"VIKOR method for Pythagorean hesitant fuzzy multi-attribute decision-making based on regret theory","volume":"126","author":"Zhang","year":"2023","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"101802","DOI":"10.1016\/j.aei.2022.101802","article-title":"An evolved VIKOR method for multiple-criteria compromise ranking modeling under T-spherical fuzzy uncertainty","volume":"54","author":"Chen","year":"2022","journal-title":"Adv. Eng. Inform."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1532","DOI":"10.1016\/j.ins.2022.06.037","article-title":"Multiattribute decision making based on Fermatean hesitant fuzzy sets and modified VIKOR method","volume":"607","author":"Mishra","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.ins.2021.03.039","article-title":"A new classification and ranking decision method based on three-way decision theory and TOPSIS models","volume":"568","author":"Zhang","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1016\/j.ejor.2024.01.043","article-title":"Three-way decisions based multi-attribute decision-making with utility and loss functions","volume":"316","author":"Bisht","year":"2024","journal-title":"Eur. J. Oper. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"120309","DOI":"10.1016\/j.ins.2024.120309","article-title":"Optimized third-generation prospect theory-based three-way decision approach for conflict analysis in multi-scale Z-number information systems","volume":"663","author":"Wang","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1007\/s13042-020-01082-x","article-title":"Complex network analysis of three-way decision researches","volume":"11","author":"Yang","year":"2020","journal-title":"Int. J. Mach. Learn. Cybern."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.ins.2022.10.107","article-title":"A three-way decision approach with prospect-regret theory via fuzzy set pair dominance degrees for incomplete information systems","volume":"617","author":"Zhan","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.ins.2022.02.036","article-title":"Integration of semantic patterns and fuzzy concepts to reduce the boundary region in three-way decision-making","volume":"595","author":"Subhashini","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"111171","DOI":"10.1016\/j.asoc.2023.111171","article-title":"A three-way conflict analysis model with decision makers\u2019 varying preferences","volume":"151","author":"Jiang","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"111315","DOI":"10.1016\/j.asoc.2024.111315","article-title":"Three-way multi-attribute decision-making under the double hierarchy hesitant fuzzy linguistic information system","volume":"154","author":"Luo","year":"2024","journal-title":"Appl. Soft Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"110353","DOI":"10.1016\/j.asoc.2023.110353","article-title":"An attribute fuzzy concept-oriented three-way utility decision model in multi-attribute environments","volume":"143","author":"Qi","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.ins.2022.10.014","article-title":"Generalized multigranulation sequential three-way decision models for hierarchical classification","volume":"616","author":"Qian","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"118370","DOI":"10.1016\/j.eswa.2022.118370","article-title":"A three-way decision approach with S-shaped utility function under Pythagorean fuzzy information","volume":"210","author":"Yi","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.ins.2021.12.079","article-title":"A three-way decision approach with risk strategies in hesitant fuzzy decision information systems","volume":"588","author":"Wang","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"109522","DOI":"10.1016\/j.knosys.2022.109522","article-title":"A novel interval-valued three-way decision theory under multiple criteria environment","volume":"253","author":"Pan","year":"2022","journal-title":"Knowl.-Based Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"120443","DOI":"10.1016\/j.ins.2024.120443","article-title":"A novel three-way classification and ranking approach based on regret theory and TOPSIS","volume":"666","author":"Yan","year":"2024","journal-title":"Inf. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.ins.2020.05.060","article-title":"A multilevel neighborhood sequential decision approach of three-way granular computing","volume":"538","author":"Yang","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"110978","DOI":"10.1016\/j.asoc.2023.110978","article-title":"A sequential three-way classification model based on risk preference and decision correction","volume":"149","author":"Liang","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.ins.2019.06.003","article-title":"Granularity-driven sequential three-way decisions: A cost-sensitive approach to classification","volume":"507","author":"Fang","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.knosys.2018.08.022","article-title":"Sequential three-way classifier with justifiable granularity","volume":"163","author":"Ju","year":"2019","journal-title":"Knowl.-Based Syst."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yao, Y. (2013). Granular computing and sequential three-way decisions. International Conference on Rough Sets and Knowledge Technology, Springer.","DOI":"10.1007\/978-3-642-41299-8_3"},{"key":"ref_25","unstructured":"Yao, Y. (2015). Rough sets and three-way decisions. Rough Sets and Knowledge Technology: 10th International Conference, RSKT 2015, Held as Part of the International Joint Conference on Rough Sets, IJCRS 2015, Tianjin, China, 20\u201323 November 2015, Proceedings 10, Springer International Publishing."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yao, Y., and Deng, X. (2011, January 18\u201320). Sequential Three-Way Decisions with Probabilistic Rough Sets. Proceedings of the 10th IEEE International Conference on Cognitive Informatics and Cognitive Computing, Banff, AB, Canada.","DOI":"10.1109\/COGINF.2011.6016129"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.knosys.2017.07.031","article-title":"A unified model of sequential three-way decisions and multilevel incremental processing","volume":"134","author":"Yang","year":"2017","journal-title":"Knowl.-Based Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.ejor.2006.01.020","article-title":"Extended VIKOR method in comparison with outranking methods","volume":"178","author":"Opricovic","year":"2007","journal-title":"Eur. J. Oper. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1016\/j.ins.2020.06.050","article-title":"A novel decision-making approach based on three-way decisions in fuzzy information systems","volume":"541","author":"Ye","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.ins.2018.08.051","article-title":"A novel three-way decision model under multiple-criteria environment","volume":"471","author":"Jia","year":"2019","journal-title":"Inf. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/j.ins.2022.06.018","article-title":"BMW-TOPSIS: A generalized TOPSIS model based on three-way decision","volume":"607","author":"Wang","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"105048","DOI":"10.1016\/j.engappai.2022.105048","article-title":"Decision making framework based Fermatean fuzzy integrated weighted distance and TOPSIS for green low-carbon port evaluation","volume":"114","author":"Wang","year":"2022","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1086\/257678","article-title":"Cardinal welfare, individualistic ethics, and interpersonal comparisons of utility","volume":"63","author":"Harsanyi","year":"1955","journal-title":"J. Political Econ."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"435","DOI":"10.15388\/Informatica.2015.57","article-title":"Multi-criteria inventory classification using a new method of evaluation based on distance from average solution (EDAS)","volume":"26","author":"Mehdi","year":"2015","journal-title":"Informatica"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/11\/530\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:35:03Z","timestamp":1760114103000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/11\/530"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,19]]},"references-count":34,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2024,11]]}},"alternative-id":["a17110530"],"URL":"https:\/\/doi.org\/10.3390\/a17110530","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,19]]}}}