{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:16:17Z","timestamp":1760242577771,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2017,10,27]],"date-time":"2017-10-27T00:00:00Z","timestamp":1509062400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Through the combination of different types of sets such as fuzzy sets, soft sets and rough sets, abundant hybrid models have been presented in order to take advantage of each other and handle uncertainties. A comparative study of relationships and interconnections of some existing hybrid models has been carried out. Some foundational properties of modified soft rough sets (MSR sets) are analyzed. It is pointed out that MSR approximation operators are some kinds of Pawlak approximation operators, whereas approximation operators of Z-soft rough fuzzy sets are equivalent to approximation operators of rough fuzzy sets. The relationships among F-soft rough fuzzy sets, M-soft rough fuzzy sets and Z-soft rough fuzzy sets are surveyed. A new model called soft rough soft sets has been provided as the generalization of F-soft rough sets, and its application in group decision-making has been studied. Various soft rough sets models show great potential as a tool to solve decision-making problems, and a depth study of the connections among these models contributes to the flexible application of soft rough sets based decision-making approaches.<\/jats:p>","DOI":"10.3390\/sym9110252","type":"journal-article","created":{"date-parts":[[2017,10,27]],"date-time":"2017-10-27T11:33:28Z","timestamp":1509104008000},"page":"252","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Comparative Study of Some Soft Rough Sets"],"prefix":"10.3390","volume":"9","author":[{"given":"Yaya","family":"Liu","sequence":"first","affiliation":[{"name":"College of Mathematics, Southwest Jiaotong University, Chengdu 610031, China"},{"name":"Department of Computer Science, University of Ja\u00e9n, E-23071 Ja\u00e9n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4245-8813","authenticated-orcid":false,"given":"Luis","family":"Mart\u00ednez","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Ja\u00e9n, E-23071 Ja\u00e9n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keyun","family":"Qin","sequence":"additional","affiliation":[{"name":"College of Mathematics, Southwest Jiaotong University, Chengdu 610031, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,10,27]]},"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. Control"},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.ins.2006.06.003","article-title":"Rudiments of rough sets","volume":"177","author":"Pawlak","year":"2007","journal-title":"Inf. Sci."},{"key":"ref_4","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":"Comput. Math. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1016\/j.camwa.2010.05.036","article-title":"Interval-valued intuitionistic fuzzy soft sets and their properties","volume":"60","author":"Jiang","year":"2010","journal-title":"Comput. Math. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1080\/03081079008935107","article-title":"Rough fuzzy set and fuzzy rough sets","volume":"17","author":"Dubois","year":"1990","journal-title":"Int. J. Gen. Syst."},{"key":"ref_7","first-page":"589","article-title":"Fuzzy soft sets","volume":"9","author":"Maji","year":"2001","journal-title":"J. Fuzzy Math."},{"key":"ref_8","first-page":"669","article-title":"On intuitionistic fuzzy soft sets","volume":"12","author":"Maji","year":"2004","journal-title":"J. Fuzzy Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"569","DOI":"10.2991\/ijcis.2017.10.1.39","article-title":"A theoretical development on the entropy of interval-valued intuitionistic fuzzy soft sets based on the distance measure","volume":"10","author":"Liu","year":"2017","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1016\/j.camwa.2009.10.015","article-title":"Vague soft sets and their properties","volume":"59","author":"Xu","year":"2010","journal-title":"Comput. Math. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1080\/18756891.2013.773192","article-title":"Combination of interval set and soft set","volume":"2","author":"Qin","year":"2013","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"899","DOI":"10.1007\/s00500-009-0465-6","article-title":"Soft sets combined with fuzzy sets and rough sets: A tentative approach","volume":"14","author":"Feng","year":"2010","journal-title":"Soft Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1016\/j.ins.2010.11.004","article-title":"Soft sets and soft rough sets","volume":"181","author":"Feng","year":"2011","journal-title":"Inf. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4635","DOI":"10.1016\/j.camwa.2011.10.049","article-title":"Soft rough fuzzy sets and soft fuzzy rough sets","volume":"62","author":"Meng","year":"2011","journal-title":"Comput. Math. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Li, T., Nguyen, H.S., Wang, G., Grzymala-Busse, J.W., Janicki, R., Hassanien, A.-E., and Yu, H. (2012). Soft rough sets based on similarity measures. Rough Sets and Knowledge Technology, Springer. RSKT 2012.","DOI":"10.1007\/978-3-642-31900-6"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.knosys.2012.11.012","article-title":"Another approach to soft rough sets","volume":"40","author":"Shabir","year":"2013","journal-title":"Knowl.-Based Syst."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1923","DOI":"10.1007\/s00500-016-2119-9","article-title":"A novel soft rough fuzzy sets: Z-soft rough fuzzy ideals of hemirings and corresponding decision-making","volume":"21","author":"Zhan","year":"2017","journal-title":"Soft Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"394","DOI":"10.2991\/ijcis.2017.10.1.27","article-title":"A New Criterion for Soft Set Based Decision Making Problems under Incomplete Information","volume":"10","author":"Alcantud","year":"2017","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1016\/j.asoc.2017.06.010","article-title":"Separable fuzzy soft sets and decision-making with positive and negative attributes","volume":"59","author":"Alcantud","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.asoc.2016.09.012","article-title":"A novel soft rough set: Soft rough hemirings and its multicriteria group decision-making","volume":"54","author":"Zhan","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/j.asoc.2017.03.038","article-title":"On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods","volume":"56","author":"Zhan","year":"2017","journal-title":"Appl. Soft Comput."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1016\/j.apm.2016.04.014","article-title":"A novel approach to multi attribute group decision-making based on trapezoidal interval type-2 fuzzy soft sets","volume":"41","author":"Khalil","year":"2016","journal-title":"Appl. Math. Model."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1803","DOI":"10.3233\/IFS-151892","article-title":"A method for multi-attribute decision-making applying soft rough sets","volume":"30","author":"Zhang","year":"2016","journal-title":"J. Intell. Fuzzy Syst."},{"key":"ref_24","first-page":"1248","article-title":"An algorithm for multi-attribute decision-making based on soft rough sets","volume":"20","author":"Yu","year":"2016","journal-title":"J. Comput. Anal. Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1547","DOI":"10.1016\/j.camwa.2008.11.009","article-title":"On some new operations in soft set theory","volume":"57","author":"Ali","year":"2009","journal-title":"Comput. Math. Appl."},{"key":"ref_26","unstructured":"Pei, D., and Miao, D. (2005, January 25\u201327). From soft sets to information systems. Proceedings of the 2005 IEEE International Conference on Granular Computing, Beijing, China."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3329","DOI":"10.1016\/j.asoc.2011.01.003","article-title":"A note on soft sets, rough soft sets and fuzzy soft sets","volume":"11","author":"Ali","year":"2011","journal-title":"Appl. Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0020-0255(02)00379-1","article-title":"Generalized fuzzy rough sets","volume":"151","author":"Wu","year":"2003","journal-title":"Inf. Sci."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/S0020-0255(98)10006-3","article-title":"Relational interpretations of neighborhood operators and rough set approximation operators","volume":"111","author":"Yao","year":"1998","journal-title":"Inf. Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.ins.2008.09.015","article-title":"Relationship between generalized rough sets based on binary relation and covering","volume":"179","author":"Zhu","year":"2009","journal-title":"Inf. Sci."},{"key":"ref_31","first-page":"69","article-title":"Soft rough sets applied to multicriteria group decision-making","volume":"2","author":"Feng","year":"2011","journal-title":"Ann. Fuzzy Math. Inf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s10462-011-9298-7","article-title":"Soft fuzzy rough sets and its application in decision-making","volume":"41","author":"Sun","year":"2014","journal-title":"Artif. Intell. Rev."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Rival, I. (1982). Restructuring lattice theory: An approach based on hierarchies of concepts. Ordered Sets, Reidel Dordrecht.","DOI":"10.1007\/978-94-009-7798-3"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Polkowski, L., Yao, Y., Artiermjew, P., Ciucci, D., Liu, D., \u015al\u0119zak, D., and Zielo sko, B. (2017). Attribute Reduction in Rough Set Theory and Formal Concept Analysis. Rough Sets, Springer. IJCRS 2017.","DOI":"10.1007\/978-3-319-60837-2"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/j.ins.2014.12.010","article-title":"Concept learning via granular computing: A cognitive viewpoint","volume":"298","author":"Li","year":"2015","journal-title":"Inf. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1080\/18756891.2015.1001951","article-title":"Roughness of fuzzy soft sets and related results","volume":"8","author":"Li","year":"2015","journal-title":"Int. J. Comput. Intell. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0165-0114(92)90090-Q","article-title":"Soft sets: An ordinal formulation of vagueness with some applications to the theory of choice","volume":"45","author":"Basu","year":"1992","journal-title":"Fuzzy Sets Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/11\/252\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:48:39Z","timestamp":1760208519000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/11\/252"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10,27]]},"references-count":37,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2017,11]]}},"alternative-id":["sym9110252"],"URL":"https:\/\/doi.org\/10.3390\/sym9110252","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2017,10,27]]}}}