{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:46Z","timestamp":1760240026471,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,19]],"date-time":"2019-02-19T00:00:00Z","timestamp":1550534400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51508319"],"award-info":[{"award-number":["51508319"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Based on comparative studies on correlation coefficient theory and utility theory, a series of rules that utility functions on dual hesitant fuzzy rough sets (DHFRSs) should satisfy, and a kind of novel utility function on DHFRSs are proposed. The characteristic of the introduced utility function is a parameter, which is determined by decision-makers according to their experiences. By using the proposed utility function on DHFRSs, a novel dual hesitant fuzzy rough pattern recognition method is also proposed. Furthermore, this study also points out that the classical dual tool is suitable to cope with dynamic data in exploratory data analysis situations, while the newly proposed one is suitable to cope with static data in confirmatory data analysis situations. Finally, a medical diagnosis and a traffic engineering example are introduced to reveal the effectiveness of the newly proposed utility functions on DHFRSs.<\/jats:p>","DOI":"10.3390\/info10020071","type":"journal-article","created":{"date-parts":[[2019,2,20]],"date-time":"2019-02-20T03:05:52Z","timestamp":1550631952000},"page":"71","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Novel Parameterized Utility Function on Dual Hesitant Fuzzy Rough Sets and Its Application in Pattern Recognition"],"prefix":"10.3390","volume":"10","author":[{"given":"Zhongjun","family":"Wu","sequence":"first","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5798-5662","authenticated-orcid":false,"given":"Fangwei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Transportation, Southeast University, Nanjing 210096, China"},{"name":"College of Transport and Communications, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Macau, Macau 999078, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4024-7684","authenticated-orcid":false,"given":"Wenjing","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xufeng","family":"Tang","sequence":"additional","affiliation":[{"name":"College of Transport and Communications, Shanghai Maritime University, Shanghai 201306, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","article-title":"Fuzzy sets","volume":"8","author":"Zadeh","year":"1965","journal-title":"Inf. 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Soft Computing and Human-Centered Machines, Springer.","DOI":"10.1007\/978-4-431-67907-3_2"},{"key":"ref_7","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_8","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":"2010","journal-title":"Inf. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1016\/j.ijar.2011.12.010","article-title":"Probabilistic rough set over two universes and rough entropy","volume":"53","author":"Ma","year":"2012","journal-title":"Int. J. Approx. Reason."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1079","DOI":"10.1057\/jors.2012.75","article-title":"An approach to decision making based on intuitionistic fuzzy rough sets over two universes","volume":"64","author":"Sun","year":"2013","journal-title":"J. Oper. Res. Soc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"817","DOI":"10.1016\/j.knosys.2010.05.006","article-title":"Research on the model of rough set over dual-universes","volume":"23","author":"Yan","year":"2010","journal-title":"Knowl. Based Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.knosys.2012.01.001","article-title":"Bipolar fuzzy rough set model on two different universes and its application","volume":"35","author":"Yang","year":"2012","journal-title":"Knowl. Based Syst."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.knosys.2011.07.012","article-title":"Transformation of bipolar fuzzy rough set models","volume":"27","author":"Yang","year":"2012","journal-title":"Knowl. Based Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1080\/03081079008935107","article-title":"Rough fuzzy sets and fuzzy rough sets","volume":"17","author":"Dubois","year":"1990","journal-title":"Int. J. Gen. Syst."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/S0165-0114(01)00032-X","article-title":"A comparative study of fuzzy rough sets","volume":"126","author":"Radzikowska","year":"2002","journal-title":"Fuzzy Sets Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.fss.2013.03.005","article-title":"Fuzzy rough set model for set-valued data","volume":"229","author":"Dai","year":"2013","journal-title":"Fuzzy Sets Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.fss.2012.06.001","article-title":"Fuzzy rough sets, fuzzy preorders and fuzzy topologies","volume":"210","author":"Tiwari","year":"2013","journal-title":"Fuzzy Sets Syst."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1007\/s00500-013-1127-2","article-title":"Constructive and axiomatic approaches to hesitant fuzzy rough set","volume":"18","author":"Yang","year":"2014","journal-title":"Soft Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3287","DOI":"10.1007\/s00500-015-2008-7","article-title":"Dual hesitant fuzzy rough set and its application","volume":"21","author":"Zhang","year":"2015","journal-title":"Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s40815-015-0012-9","article-title":"Generalized interval-valued fuzzy rough set and its application in decision making","volume":"17","author":"Zhang","year":"2015","journal-title":"Int. J. Fuzzy Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"121","DOI":"10.31181\/dmame1801121r","article-title":"A rough strength relational DEMATEL model for analysing the key success factors of hospital service quality","volume":"1","author":"Roy","year":"2018","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"82","DOI":"10.31181\/dmame180182v","article-title":"A rough multicriteria approach for evaluation of supplier criteria in automotive industry","volume":"1","author":"Vasiljevic","year":"2018","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.jclepro.2018.02.186","article-title":"Evaluating the performance of suppliers based on using the R\u2019AMATEL-MAIRCA method for green supply chain implementation in electronics industry","volume":"184","author":"Chatterjee","year":"2018","journal-title":"J. Clean. Prod."},{"key":"ref_24","first-page":"171","article-title":"Normalized weighted geometric bonferroni mean operator of interval rough numbers\u2014application in interval rough DEMATEL-COPRAS","volume":"16","author":"Pamucar","year":"2018","journal-title":"Mech. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.asoc.2018.02.057","article-title":"Integration of interval rough AHP and interval rough MABAC methods for evaluating university web pages","volume":"67","author":"Pamucar","year":"2018","journal-title":"Appl. Soft Comput."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.eswa.2017.08.042","article-title":"Modification of the Best\u2013Worst and MABAC methods: A novel approach based on interval-valued fuzzy-rough numbers","volume":"91","author":"Pamucar","year":"2018","journal-title":"Expert Syst. Appl."},{"key":"ref_27","unstructured":"Zhang, F.W. (2016). Several Kinds of Uncertain Multi-Attribute Decision-Making Methods and Their Application in Transportation Management, People\u2019s Communication Press."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"51","DOI":"10.31181\/dmame1802050m","article-title":"A sensitivity analysis in MCDM problems: A statistical approach","volume":"1","author":"Mukhametzyanov","year":"2018","journal-title":"Decis. Mak. Appl. Manag. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1007\/s10726-016-9473-y","article-title":"Multiple attribute group decision making method based on utility theory under interval-valued intuitionistic fuzzy environment","volume":"25","author":"Zhang","year":"2016","journal-title":"Group Decis. Negotiat."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Szmidt, E., and Kacprzyk, J. (2002). An intuitionistic fuzzy set based approach to intelligent data analysis: An application to medical diagnosis. Recent Advances in Intelligent Paradigms and and Applications, Springer.","DOI":"10.1007\/978-3-7908-1770-6_3"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"147","DOI":"10.20965\/jaciii.2018.p0147","article-title":"Entropy analysis on intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets and its applications in mode assessment on open communities","volume":"22","author":"Tian","year":"2018","journal-title":"J. Adv. Comput. Intell. Intell. Inform."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1958","DOI":"10.1109\/TITS.2016.2613997","article-title":"A unified framework for vehicle rerouting and traffic light control to reduce traffic congestion","volume":"18","author":"Cao","year":"2017","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1688","DOI":"10.1109\/TITS.2015.2498160","article-title":"Finding the shortest path in stochastic vehicle routing: A cardinality minimization approach","volume":"17","author":"Cao","year":"2016","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_34","first-page":"25","article-title":"A multiagent-based approach for vehicle routing by considering both arriving on time and total travel time","volume":"18","author":"Cao","year":"2018","journal-title":"ACM Trans. Intell. Syst. Technol."},{"key":"ref_35","unstructured":"Cao, Z., Wu, Y., Rao, A., Klanner, F., Erschen, S., Chen, W., Zhang, L., and Guo, H. (2018). An accurate solution to the cardinality-based punctuality problem. IEEE Intell. Transp. Syst. Mag."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1515\/acsc-2017-0024","article-title":"Dual hesitant Pythagorean fuzzy Hamacher aggregation operators in multiple attribute decision making","volume":"27","author":"Wei","year":"2017","journal-title":"Arch. Control Sci."}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/10\/2\/71\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:33:21Z","timestamp":1760186001000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/10\/2\/71"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,19]]},"references-count":36,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["info10020071"],"URL":"https:\/\/doi.org\/10.3390\/info10020071","relation":{},"ISSN":["2078-2489"],"issn-type":[{"type":"electronic","value":"2078-2489"}],"subject":[],"published":{"date-parts":[[2019,2,19]]}}}