{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T07:40:23Z","timestamp":1778744423197,"version":"3.51.4"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2016,3,31]],"date-time":"2016-03-31T00:00:00Z","timestamp":1459382400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61370053, 61370193, and 61572081"],"award-info":[{"award-number":["61370053, 61370193, and 61572081"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2017,5]]},"DOI":"10.1007\/s00500-016-2133-y","type":"journal-article","created":{"date-parts":[[2016,3,31]],"date-time":"2016-03-31T08:35:54Z","timestamp":1459413354000},"page":"2189-2199","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A unified view of consistent functions"],"prefix":"10.1007","volume":"21","author":[{"given":"Ping","family":"Zhu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huiyang","family":"Xie","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiaoyan","family":"Wen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,3,31]]},"reference":[{"key":"2133_CR1","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.neunet.2013.07.008","volume":"48","author":"A Ganivada","year":"2013","unstructured":"Ganivada A, Ray SS, Pal SK (2013) Fuzzy rough sets, and a granular neural network for unsupervised feature selection. Neur Netw 48:91\u2013108","journal-title":"Neur Netw"},{"issue":"7","key":"2133_CR2","doi-asserted-by":"publisher","first-page":"1973","DOI":"10.1007\/s00500-014-1382-x","volume":"19","author":"H Ge","year":"2015","unstructured":"Ge H, Li L, Xu Y, Yang C (2015) Bidirectional heuristic attribute reduction based on conflict region. Soft Comput 19(7):1973\u20131986","journal-title":"Soft Comput"},{"issue":"2","key":"2133_CR3","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1080\/03081070903463544","volume":"39","author":"ZT Gong","year":"2010","unstructured":"Gong ZT, Xiao ZY (2010) Communicating between information systems based on including degrees. Int J Gen Syst 39(2):189\u2013206","journal-title":"Int J Gen Syst"},{"key":"2133_CR4","doi-asserted-by":"publisher","unstructured":"Grzymala-Busse J (1986) Algebraic properties of knowledge representation systems. In: Proceedings of the ACM SIGART international symposium on methodologies for intelligent systems, ACM, pp 432\u2013440","DOI":"10.1145\/12808.12856"},{"issue":"3","key":"2133_CR5","first-page":"233","volume":"36","author":"J Grzymala-Busse","year":"1988","unstructured":"Grzymala-Busse J, Sedelow W Jr (1988) On rough sets and information system homomorphism. Bull Pol Acad Sci Tech Sci 36(3):233\u2013239","journal-title":"Bull Pol Acad Sci Tech Sci"},{"key":"2133_CR6","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1007\/3-540-45631-7_3","volume-title":"Advances in soft computing-AFSS 2002, Lecture Notes in Computer Science","author":"R Intan","year":"2002","unstructured":"Intan R, Mukaidono M (2002) Degree of similarity in fuzzy partition. In: Pal NR, Sugeno M (eds) Advances in soft computing-AFSS 2002, Lecture Notes in Computer Science, vol 2275. Springer, Berlin, pp 20\u201326"},{"key":"2133_CR7","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/S0020-0255(00)00017-7","volume":"129","author":"DY Li","year":"2000","unstructured":"Li DY, Ma Y (2000) Invariant characters of information systems under some homomorphisms. Inf Sci 129:211\u2013220","journal-title":"Inf Sci"},{"key":"2133_CR8","doi-asserted-by":"crossref","unstructured":"Lin TY (1989b) Chinese wall security policy-an aggressive model. In: Proceedings of the fifth annual computer security applications conference, pp 282\u2013289","DOI":"10.1109\/CSAC.1989.81064"},{"key":"2133_CR9","unstructured":"Lin TY (1989b) Neighborhood systems and approximation in relational databases and knowledge bases. In: Proceedings of the fourth international symposium on methodologies of intelligent systems, pp 75\u201386"},{"key":"2133_CR10","unstructured":"Lin TY (1997) Granular computing: From rough sets and neighborhood systems to information granulation and computing in words. In: European congress on intelligent techniques and soft computing, pp 1602\u20131606"},{"key":"2133_CR11","unstructured":"Lin TY (2009) The \u201cfinal\u201d model of granular computing. In: IEEE international conference on fuzzy systems, IEEE, pp 1523\u20131528"},{"key":"2133_CR12","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1016\/j.fss.2014.01.015","volume":"258","author":"V L\u00f3pez","year":"2014","unstructured":"L\u00f3pez V, del R\u00edo S, Ben\u00edtez JM, Herrera F (2014) Cost-sensitive linguistic fuzzy rule based classification systems under the mapreduce framework for imbalanced big data. Fuzzy Sets Syst 258:5\u201338","journal-title":"Fuzzy Sets Syst"},{"key":"2133_CR13","volume-title":"Information granularity, big data, and computational intelligence, studies in big data","year":"2015","unstructured":"Pedrycz W, Chen SM (eds) (2015) Information granularity, big data, and computational intelligence, studies in big data, vol 8. Springer, Berlin"},{"issue":"11","key":"2133_CR14","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1002\/1098-111X(200011)15:11<1015::AID-INT3>3.0.CO;2-9","volume":"15","author":"W Pedrycz","year":"2000","unstructured":"Pedrycz W, Vukovich G (2000) Granular worlds: representation and communication problems. Int J Intell Syst 15(11):1015\u20131026","journal-title":"Int J Intell Syst"},{"issue":"10","key":"2133_CR15","doi-asserted-by":"publisher","first-page":"2751","DOI":"10.1007\/s00500-014-1439-x","volume":"19","author":"W Pedrycz","year":"2015","unstructured":"Pedrycz W, Al-Hmouz R, Morfeq A, Balamash A (2015) Distributed proximity-based granular clustering: towards a development of global structural relationships in data. Soft Comput 19(10):2751\u20132767","journal-title":"Soft Comput"},{"key":"2133_CR16","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.fss.2014.04.029","volume":"258","author":"Y Qian","year":"2014","unstructured":"Qian Y, Wang Q, Cheng H, Liang J, Dang C (2014) Fuzzy-rough feature selection accelerator. Fuzzy Sets Syst 258:61\u201378","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"2133_CR17","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/S0019-9958(69)90591-9","volume":"15","author":"EH Ruspini","year":"1969","unstructured":"Ruspini EH (1969) A new approach to clustering. Inf Contr 15(1):22\u201332","journal-title":"Inf Contr"},{"key":"2133_CR18","volume-title":"General topology","author":"W Sierpi\u0144ski","year":"1956","unstructured":"Sierpi\u0144ski W, Krieger CC (1956) General topology. University of Toronto, Toronto"},{"issue":"3","key":"2133_CR19","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1109\/TFUZZ.2012.2218658","volume":"21","author":"ECC Tsang","year":"2013","unstructured":"Tsang ECC, Wang C, Chen D, Wu C, Hu Q (2013) Communication between information systems using fuzzy rough sets. IEEE Trans Fuzzy Syst 21(3):527\u2013540","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"2133_CR20","doi-asserted-by":"publisher","first-page":"940","DOI":"10.1016\/j.aml.2007.10.006","volume":"21","author":"C Wang","year":"2008","unstructured":"Wang C, Wu C, Chen D, Du W (2008a) Some properties of relation information systems under homomorphisms. Appl Math Lett 21:940\u2013945","journal-title":"Appl Math Lett"},{"key":"2133_CR21","doi-asserted-by":"publisher","first-page":"3228","DOI":"10.1016\/j.ins.2008.03.017","volume":"178","author":"C Wang","year":"2008","unstructured":"Wang C, Wu C, Chen D, Hu Q, Wu C (2008b) Communicating between information systems. Inf Sci 178:3228\u20133239","journal-title":"Inf Sci"},{"key":"2133_CR22","doi-asserted-by":"publisher","first-page":"1045","DOI":"10.1016\/j.aml.2009.01.013","volume":"22","author":"C Wang","year":"2009","unstructured":"Wang C, Chen D, Zhu L (2009) Homomorphisms between fuzzy information systems. Appl Math Lett 22:1045\u20131050","journal-title":"Appl Math Lett"},{"issue":"9","key":"2133_CR23","doi-asserted-by":"publisher","first-page":"1816","DOI":"10.1007\/s11432-010-4044-3","volume":"53","author":"C Wang","year":"2010","unstructured":"Wang C, Chen D, Hu Q (2010) Some invariant properties of ordered information systems under homomorphism. Sci China Inf Sci 53(9):1816\u20131825","journal-title":"Sci China Inf Sci"},{"issue":"4","key":"2133_CR24","doi-asserted-by":"publisher","first-page":"519","DOI":"10.1016\/j.ijar.2010.11.009","volume":"52","author":"C Wang","year":"2011","unstructured":"Wang C, Chen D, Wu C, Hu Q (2011) Data compression with homomorphism in covering information systems. Int J Approx Reason 52(4):519\u2013525","journal-title":"Int J Approx Reason"},{"key":"2133_CR25","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.ins.2012.06.010","volume":"216","author":"C Wang","year":"2012","unstructured":"Wang C, Chen D, Sun B, Hu Q (2012) Communication between information systems with covering based rough sets. Inf Sci 216:17\u201333","journal-title":"Inf Sci"},{"key":"2133_CR26","doi-asserted-by":"publisher","first-page":"128","DOI":"10.1016\/j.fss.2014.02.009","volume":"249","author":"C Wang","year":"2014","unstructured":"Wang C, Chen D, Hu Q (2014) Fuzzy information systems and their homomorphisms. Fuzzy Sets Syst 249:128\u2013138","journal-title":"Fuzzy Sets Syst"},{"key":"2133_CR27","doi-asserted-by":"publisher","unstructured":"Yang X, Li X, Lin TY (2009) First grc model-neighborhood systems the most general rough set models. In: IEEE international conference on granular computing, GrC\u201909, pp 691\u2013695","DOI":"10.1109\/GRC.2009.5255031"},{"key":"2133_CR28","first-page":"232","volume-title":"A partition model of granular computing. Lecture Notes in Computer Science","author":"YY Yao","year":"2004","unstructured":"Yao YY (2004) A partition model of granular computing. Lecture Notes in Computer Science, vol 3100. Springer, Berlin, pp 232\u2013253"},{"issue":"7","key":"2133_CR29","doi-asserted-by":"publisher","first-page":"1893","DOI":"10.1007\/s00500-014-1371-0","volume":"19","author":"D Ye","year":"2015","unstructured":"Ye D, Chen Z (2015) A new approach to minimum attribute reduction based on discrete artificial bee colony. Soft Comput 19(7):1893\u20131903","journal-title":"Soft Comput"},{"issue":"2","key":"2133_CR30","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/S0165-0114(97)00077-8","volume":"90","author":"LA Zadeh","year":"1997","unstructured":"Zadeh LA (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 90(2):111\u2013127","journal-title":"Fuzzy Sets Syst"},{"issue":"3","key":"2133_CR31","doi-asserted-by":"publisher","first-page":"414","DOI":"10.1007\/s00224-007-9076-8","volume":"44","author":"Y Zhai","year":"2009","unstructured":"Zhai Y, Qu K (2009) On characteristics of information system homomorphisms. Theory Comput Syst 44(3):414\u2013431","journal-title":"Theory Comput Syst"},{"key":"2133_CR32","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.ins.2014.09.007","volume":"292","author":"X Zhang","year":"2015","unstructured":"Zhang X, Dai J, Yu Y (2015) On the union and intersection operations of rough sets based on various approximation spaces. Inf Sci 292:214\u2013229","journal-title":"Inf Sci"},{"issue":"6","key":"2133_CR33","doi-asserted-by":"publisher","first-page":"1567","DOI":"10.1007\/s00500-014-1307-8","volume":"19","author":"L Zheng","year":"2015","unstructured":"Zheng L, Diao R, Shen Q (2015) Self-adjusting harmony search-based feature selection. Soft Comput 19(6):1567\u20131579","journal-title":"Soft Comput"},{"issue":"18","key":"2133_CR34","doi-asserted-by":"publisher","first-page":"3521","DOI":"10.1016\/j.ins.2010.05.028","volume":"180","author":"P Zhu","year":"2010","unstructured":"Zhu P, Wen Q (2010) Some improved results on communication between information systems. Inf Sci 180(18):3521\u20133531","journal-title":"Inf Sci"},{"key":"2133_CR35","doi-asserted-by":"publisher","first-page":"1548","DOI":"10.1016\/j.aml.2011.03.044","volume":"24","author":"P Zhu","year":"2011","unstructured":"Zhu P, Wen Q (2011a) Homomorphisms between fuzzy information systems revisited. Appl Math Lett 24:1548\u20131553","journal-title":"Appl Math Lett"},{"issue":"8","key":"2133_CR36","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1080\/03081079.2011.611805","volume":"40","author":"P Zhu","year":"2011","unstructured":"Zhu P, Wen Q (2011b) A note on communicating between information systems based on including degrees. Int J Gen Syst 40(8):837\u2013840","journal-title":"Int J Gen Syst"},{"key":"2133_CR37","first-page":"331","volume":"135","author":"P Zhu","year":"2014","unstructured":"Zhu P, Xie H, Wen Q (2014) A unified definition of consistent functions. Fund Inf 135:331\u2013340","journal-title":"Fund Inf"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-016-2133-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-016-2133-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-016-2133-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-016-2133-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T01:54:52Z","timestamp":1748829292000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-016-2133-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3,31]]},"references-count":37,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2017,5]]}},"alternative-id":["2133"],"URL":"https:\/\/doi.org\/10.1007\/s00500-016-2133-y","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3,31]]}}}