{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T22:19:58Z","timestamp":1769120398766,"version":"3.49.0"},"reference-count":45,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,15]],"date-time":"2022-05-15T00:00:00Z","timestamp":1652572800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71871229"],"award-info":[{"award-number":["71871229"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021JJ30031"],"award-info":[{"award-number":["2021JJ30031"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Hunan Provincial Natural Science Foundation of China","award":["71871229"],"award-info":[{"award-number":["71871229"]}]},{"name":"the Hunan Provincial Natural Science Foundation of China","award":["2021JJ30031"],"award-info":[{"award-number":["2021JJ30031"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the sequential three-way decision model (S3WD), conditional probability and decision threshold pair are two key elements affecting the classification results. The classical model calculates the conditional probability based on the strict equivalence relationship, which limits its application in reality. In addition, little research has studied the relationship between the threshold change and its cause at different granularity levels. To deal with these deficiencies, we propose a novel sequential three-way decision model and apply it to medical diagnosis. Firstly, we propose two methods of calculating conditional probability based on similarity relation, which satisfies the property of symmetry. Then, we construct an S3WD model for a medical information system and use three different kinds of cost functions as the basis for modifying the threshold pair at each level. Subsequently, the rule of the decision threshold pair change is explored. Furthermore, two algorithms used for implementing the proposed S3WD model are introduced. Finally, extensive experiments are carried out to validate the feasibility and effectiveness of the proposed model, and the results show that the model can achieve better classification performance.<\/jats:p>","DOI":"10.3390\/sym14051004","type":"journal-article","created":{"date-parts":[[2022,5,15]],"date-time":"2022-05-15T09:48:22Z","timestamp":1652608102000},"page":"1004","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["A Novel Sequential Three-Way Decision Model for Medical Diagnosis"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8879-4970","authenticated-orcid":false,"given":"Junhua","family":"Hu","sequence":"first","affiliation":[{"name":"School of Business, Central South University, Changsha 410083, China"}]},{"given":"Wanying","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Business, Central South University, Changsha 410083, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5377-442X","authenticated-orcid":false,"given":"Pei","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Business, Central South University, Changsha 410083, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,15]]},"reference":[{"key":"ref_1","first-page":"6","article-title":"A database for using machine learning and data mining techniques for coronary artery disease diagnosis","volume":"23","author":"Alizadehsani","year":"2019","journal-title":"Sci. Data"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Deepika, M., and Kalaiselvi, K. (2018, January 20\u201321). A Empirical study on Disease Diagnosis using Data Mining Techniques. Proceedings of the 2018 Second International Conference on Inventive Communication and Computational Technologies, Coimbatore, India.","DOI":"10.1109\/ICICCT.2018.8473185"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.neucom.2019.09.044","article-title":"BreakHis based breast cancer automatic diagnosis using deep learning: Taxonomy, survey and insights","volume":"375","author":"Benhammou","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_4","first-page":"9","article-title":"Deep learning to improve breast cancer detection on screening mammography","volume":"29","author":"Shen","year":"2019","journal-title":"Sci. Rep. UK"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.future.2019.10.043","article-title":"HealthFog: An ensemble deep learning based Smart Healthcare System for Automatic Diagnosis of Heart Diseases in integrated IoT and fog computing environments","volume":"104","author":"Tuli","year":"2020","journal-title":"Future Gener. Comp. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e12377","DOI":"10.1111\/exsy.12377","article-title":"A multiperiod hybrid decision support model for medical diagnosis and treatment based on similarities and three-way decision theory","volume":"36","author":"Yang","year":"2019","journal-title":"Expert Syst."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.knosys.2017.04.008","article-title":"Three-way decision support for diagnosis on focal liver lesions","volume":"127","author":"Chen","year":"2017","journal-title":"Knowl. Based Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/TFUZZ.2014.2360548","article-title":"Web-based medical decision support systems for three-way medical decision making with game-theoretic rough sets","volume":"23","author":"Yao","year":"2014","journal-title":"EEE Trans. Fuzzy Syst."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1016\/j.ins.2009.09.021","article-title":"Three-way decisions with probabilistic rough sets","volume":"180","author":"Yao","year":"2009","journal-title":"Inform. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yao, Y. (2009). Three-Way Decision: An Interpretation of Rules in Rough Set Theory, Springer.","DOI":"10.1007\/978-3-642-02962-2_81"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1007\/BF01001956","article-title":"Rough sets","volume":"11","author":"Pawlak","year":"1982","journal-title":"Int. J. Comput. Inf. Sci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1080","DOI":"10.1016\/j.ins.2010.11.019","article-title":"The superiority of three-way decisions in probabilistic rough set models","volume":"181","author":"Yao","year":"2010","journal-title":"Inform. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.ins.2019.05.022","article-title":"Three-way fuzzy partitions defined by shadowed sets","volume":"497","author":"Zhao","year":"2019","journal-title":"Inform. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1016\/j.ins.2018.08.024","article-title":"Three-way decisions with decision-theoretic rough sets in multiset-valued information tables","volume":"507","author":"Zhao","year":"2020","journal-title":"Inform. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.knosys.2015.09.026","article-title":"Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets","volume":"91","author":"Hu","year":"2016","journal-title":"Knowl. Based Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.ins.2014.12.036","article-title":"Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets","volume":"300","author":"Liang","year":"2015","journal-title":"Inform. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s13042-016-0591-2","article-title":"Three-way decisions model based on tolerance rough fuzzy set","volume":"8","author":"Zhai","year":"2017","journal-title":"Int. J. Mach. Learn. Cyb."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/j.ins.2018.07.065","article-title":"Fuzzy neighborhood covering for three-way classification","volume":"507","author":"Yue","year":"2020","journal-title":"Inform. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.ins.2020.03.013","article-title":"Three-way decisions of rough vague sets from the perspective of fuzziness","volume":"523","author":"Zhang","year":"2020","journal-title":"Inform. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1016\/j.knosys.2015.06.019","article-title":"Three-way recommender systems based on random forests","volume":"91","author":"Zhang","year":"2016","journal-title":"Knowl. Based Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1016\/j.ijar.2017.03.008","article-title":"Cost-sensitive sequential three-way decision modeling using a deep neural network","volume":"85","author":"Li","year":"2017","journal-title":"Int. J. Approx. Reason"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/j.knosys.2018.06.020","article-title":"A Novel three-way decision model with decision-theoretic rough sets using utility theory","volume":"159","author":"Zhang","year":"2018","journal-title":"Knowl. Based Syst."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.ins.2020.01.030","article-title":"A three-way decision model based on cumulative prospect theory","volume":"519","author":"Wang","year":"2020","journal-title":"Inform. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.knosys.2015.07.040","article-title":"Sequential three-way decision and granulation for cost-sensitive face recognition","volume":"91","author":"Li","year":"2016","journal-title":"Knowl. Based Syst."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s10844-013-0254-7","article-title":"Cost-sensitive three-way email spam filtering","volume":"42","author":"Zhou","year":"2014","journal-title":"J. Intell. Inf. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhou, B., Yao, Y., and Luo, J. (2010). A Three-Way Decision Approach to Email Spam Filtering, Springer.","DOI":"10.1007\/978-3-642-13059-5_6"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.knosys.2015.09.035","article-title":"Three-way decisions based software defect prediction","volume":"91","author":"Li","year":"2016","journal-title":"Knowl. Based Syst."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1016\/j.ins.2018.08.001","article-title":"Credit scoring using three-way decisions with probabilistic rough sets","volume":"507","author":"Maldonado","year":"2020","journal-title":"Inform. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"196","DOI":"10.1016\/j.ijar.2017.03.009","article-title":"Attribute reduction for sequential three-way decisions under dynamic granulation","volume":"85","author":"Qian","year":"2017","journal-title":"Int. J. Approx. Reason"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.ijar.2018.12.008","article-title":"Multi-objective attribute reduction in three-way decision-theoretic rough set model","volume":"105","author":"Li","year":"2019","journal-title":"Int. J. Approx. Reason"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.asoc.2017.02.033","article-title":"A multi-granulation decision-theoretic rough set method for distributed fc-decision information systems: An application in medical diagnosis","volume":"56","author":"Li","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1007\/s40815-017-0320-3","article-title":"A Novel TODIM method-based three-way decision model for medical treatment selection","volume":"20","author":"Hu","year":"2017","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"103651","DOI":"10.1016\/j.engappai.2020.103651","article-title":"A novel three-way decision method in a hybrid information system with images and its application in medical diagnosis","volume":"92","author":"Li","year":"2020","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.ijar.2020.02.010","article-title":"A model of three-way decisions for Knowledge Harnessing","volume":"120","year":"2020","journal-title":"Int. J. Approx. Reason"},{"key":"ref_35","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 & Cognitive Computing, Banff, AB, Canada.","DOI":"10.1109\/COGINF.2011.6016129"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.ijar.2018.09.005","article-title":"Three-way decision and granular computing","volume":"103","author":"Yao","year":"2018","journal-title":"Int. J. Approx. Reason"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Yao, Y. (2013). Granular Computing and Sequential Three-Way Decisions. Rough Sets and Knowledge Technology: 8th International Conference, Springer.","DOI":"10.1007\/978-3-642-41299-8_3"},{"key":"ref_38","first-page":"291","article-title":"A multifaceted analysis of probabilistic three-way decisions","volume":"132","author":"Deng","year":"2014","journal-title":"Fund Inform."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Zhang, Y. (2013, January 5\u20138). Optimizing Gini Coefficient of Probabilistic Rough Set Regions Using Game-Theoretic Rough Sets. Proceedings of the 2013 26th IEEE Canadian Conference on Electrical and Computer Engineering, Regina, SK, Canada.","DOI":"10.1109\/CCECE.2013.6567817"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.ijar.2013.03.015","article-title":"Analyzing uncertainties of probabilistic rough set regions with game-theoretic rough sets","volume":"55","author":"Azam","year":"2014","journal-title":"Int. J. Approx Reason"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.ijar.2020.02.005","article-title":"Three-Way Decision with incomplete information based on similarity and satisfiability","volume":"120","author":"Luo","year":"2020","journal-title":"Int. J. Approx. Reason"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.knosys.2015.07.036","article-title":"A novel three-way decision model based on incomplete information system","volume":"91","author":"Liu","year":"2016","journal-title":"Knowl. Based Syst."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"105350","DOI":"10.1016\/j.knosys.2019.105350","article-title":"A novel sequential three-way decisions model based on penalty function","volume":"192","author":"Zhang","year":"2019","journal-title":"Knowl. Based Syst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.ins.2017.02.038","article-title":"Three-way decisions based on decision-theoretic rough sets with dual hesitant fuzzy information","volume":"396","author":"Liang","year":"2017","journal-title":"Inform. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Yao, Y. (2007). Decision-theoretic rough set models. Rough Sets and Knowledge Technology, Springer.","DOI":"10.1007\/978-3-540-72458-2_1"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/1004\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:10:54Z","timestamp":1760137854000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/1004"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,15]]},"references-count":45,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["sym14051004"],"URL":"https:\/\/doi.org\/10.3390\/sym14051004","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,15]]}}}