{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T22:00:01Z","timestamp":1740175201563,"version":"3.37.3"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,11,30]],"date-time":"2021-11-30T00:00:00Z","timestamp":1638230400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,30]],"date-time":"2021-11-30T00:00:00Z","timestamp":1638230400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971420"],"award-info":[{"award-number":["11971420"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Fuzzy Syst."],"published-print":{"date-parts":[[2022,4]]},"DOI":"10.1007\/s40815-021-01198-4","type":"journal-article","created":{"date-parts":[[2021,11,30]],"date-time":"2021-11-30T16:58:10Z","timestamp":1638291490000},"page":"1406-1424","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fuzzy Granular Structures of Fuzzy Relation Vectors"],"prefix":"10.1007","volume":"24","author":[{"given":"Jiali","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liangdong","family":"Qu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lijun","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,30]]},"reference":[{"key":"1198_CR1","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1109\/91.493904","volume":"4","author":"LA Zadeh","year":"1996","unstructured":"Zadeh, L.A.: Fuzzy logic equals computing with words. IEEE Trans. Fuzzy Syst. 4, 103\u2013111 (1996)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1198_CR2","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/S0165-0114(97)00077-8","volume":"90","author":"LA Zadeh","year":"1997","unstructured":"Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90, 111\u2013127 (1997)","journal-title":"Fuzzy Sets Syst."},{"key":"1198_CR3","first-page":"107","volume-title":"Rough Sets In Knowledge Discovery","author":"TY Lin","year":"1998","unstructured":"Lin, T.Y.: Granular computing on binary relations I: data mining and neighborhood systems. In: Skowron, A., Polkowski, L. (eds.) Rough Sets in Knowledge Discovery, pp. 107\u2013121. Physica-Verlag, Heidelberg (1998)"},{"key":"1198_CR4","first-page":"121","volume-title":"Rough Sets In Knowledge Discovery","author":"TY Lin","year":"1998","unstructured":"Lin, T.Y.: Granular computing on binary relations II: rough set representations and belief functions. In: Skowron, A., Polkowski, L. (eds.) Rough Sets in Knowledge Discovery, pp. 121\u2013140. Physica-Verlag, Heidelberg (1998)"},{"key":"1198_CR5","unstructured":"Yao, Y.Y.: Granular computing: basic issues and possible solutions. In:  Proceedings of the Fifth International Conference on Computing and Information, vol. 1, pp. 186\u2013189 (2000)"},{"key":"1198_CR6","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1002\/1098-111X(200101)16:1<87::AID-INT7>3.0.CO;2-S","volume":"16","author":"YY Yao","year":"2001","unstructured":"Yao, Y.Y.: Information granulation and rough set approximation. Int. J. Intell. Syst. 16, 87\u2013104 (2001)","journal-title":"Int. J. Intell. Syst."},{"key":"1198_CR7","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1080\/0308107021000013635","volume":"31","author":"JY Liang","year":"2002","unstructured":"Liang, J.Y., Dang, C.Y., Chin, K.S., Yam Richard, C.M.: A new method for measuring uncertainty and fuzziness in rough set theory. Int. J. Gen. Syst. 31, 331\u2013342 (2002)","journal-title":"Int. J. Gen Syst"},{"key":"1198_CR8","first-page":"1427","volume":"51","author":"JY Liang","year":"2008","unstructured":"Liang, J.Y., Qian, Y.H.: Information granules and entropy theory in information systems. Sci. China (Ser. F) 51, 1427\u20131444 (2008)","journal-title":"Science in China (Series F)"},{"key":"1198_CR9","doi-asserted-by":"crossref","first-page":"4339","DOI":"10.1007\/978-0-387-30440-3_256","volume-title":"Encyclopedia of Complexity and Systems Science","author":"TY Lin","year":"2009","unstructured":"Lin, T.Y.: Granular computing: practices, theories, and future directions. In: Meyers, R.A. (ed.) Encyclopedia of Complexity and Systems Science, pp. 4339\u20134355. Springer, Berlin (2009)"},{"key":"1198_CR10","volume-title":"Theory and application of problem solving-theory and application of granular computing in quotient spaces","author":"L Zhang","year":"2007","unstructured":"Zhang, L., Zhang, B.: Theory and application of problem solving-theory and application of granular computing in quotient spaces. Tsinghua University Publishers, Beijing (2007)"},{"key":"1198_CR11","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338\u2013353 (1965)","journal-title":"Inf. Control"},{"key":"1198_CR12","first-page":"341","volume":"11","author":"Z Pawlak","year":"1982","unstructured":"Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341\u2013356 (1982)","journal-title":"Science"},{"key":"1198_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-3534-4","volume-title":"Rough sets: Theoretical aspects of reasoning about data","author":"Z Pawlak","year":"1991","unstructured":"Pawlak, Z.: Rough sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht (1991)"},{"key":"1198_CR14","doi-asserted-by":"crossref","first-page":"5365","DOI":"10.1016\/j.ins.2007.07.008","volume":"177","author":"JM Ma","year":"2007","unstructured":"Ma, J.M., Zhang, W.X., Leung, Y., Song, X.X.: Granular computing and dual Galois connection. Inf. Sci. 177, 5365\u20135377 (2007)","journal-title":"Inf. Sci."},{"issue":"10","key":"1198_CR15","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.1109\/TKDE.2008.223","volume":"21","author":"WZ Wu","year":"2009","unstructured":"Wu, W.Z., Leung, Y., Mi, J.S.: Granular computing and knowledge reduction in formal contexts. IEEE Trans. Knowl. Data Eng. 21(10), 1461\u20131474 (2009)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"1198_CR16","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/j.ijar.2008.08.004","volume":"50","author":"YH Qian","year":"2009","unstructured":"Qian, Y.H., Liang, J.Y., Dang, C.Y.: Knowledge structure, knowledge granulation and knowledge distance in a knowledge base. Int. J. Approx. Reason. 50, 174\u2013188 (2009)","journal-title":"Int. J. Approximate Reasoning"},{"key":"1198_CR17","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s10115-015-0902-z","volume":"49","author":"ZW Li","year":"2016","unstructured":"Li, Z.W., Liu, Y.Y., Li, Q.G., Qin, B.: Relationships between knowledge bases and related results. Knowl. Inf. Syst. 49, 171\u2013195 (2016)","journal-title":"Knowl. Inf. Syst."},{"issue":"6","key":"1198_CR18","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1111\/exsy.12183","volume":"33","author":"ZW Li","year":"2016","unstructured":"Li, Z.W., Li, Q.G., Zhang, R.R., Xie, N.X.: Knowledge structures in a knowledge base. Expert. Syst. 33(6), 581\u2013591 (2016)","journal-title":"Expert. Syst."},{"key":"1198_CR19","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1016\/j.ijar.2013.11.001","volume":"55","author":"YH Qian","year":"2014","unstructured":"Qian, Y.H., Zhang, H., Li, F.J., Hu, Q.H., Liang, J.Y.: Set-based granular computing: a lattice model. Int. J. Approx. Reason. 55, 834\u2013852 (2014)","journal-title":"Int. J. Approximate Reasoning"},{"key":"1198_CR20","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.ins.2018.09.048","volume":"507","author":"ZW Li","year":"2020","unstructured":"Li, Z.W., Huang, D., Liu, X.F., Xie, N.X., Zhang, G.Q.: Information structures in a covering information system. Inf. Sci. 507, 449\u2013471 (2020)","journal-title":"Inf. Sci."},{"key":"1198_CR21","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.ijar.2018.07.001","volume":"101","author":"GQ Zhang","year":"2018","unstructured":"Zhang, G.Q., Li, Z.W., Wu, W.Z., Liu, X.F., Xie, N.X.: Information structures and uncertainty measures in a fully fuzzy information system. Int. J. Approx. Reason. 101, 119\u2013149 (2018)","journal-title":"Int. J. Approximate Reasoning"},{"issue":"2","key":"1198_CR22","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1016\/j.patcog.2013.09.003","volume":"47","author":"LA Cament","year":"2014","unstructured":"Cament, L.A., Castillo, L.E., Perez, J.P., Galdames, F.J., Perez, C.A.: Fusion of local normalization and Gabor entropy weighted features for face identification. Pattern Recognit. 47(2), 568\u2013577 (2014)","journal-title":"Pattern Recognit."},{"key":"1198_CR23","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.envsoft.2015.12.011","volume":"77","author":"A Delgado","year":"2016","unstructured":"Delgado, A., Romero, I.: Environmental conflict analysis using an integrated grey clustering and entropy-weight method: a case study of a mining project in Peru. Environ. Modell. Softw. 77, 108\u2013121 (2016)","journal-title":"Environ. Modell. Softw."},{"key":"1198_CR24","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1016\/j.eswa.2015.10.023","volume":"46","author":"CF Hempelmann","year":"2016","unstructured":"Hempelmann, C.F., Sakoglu, U., Gurupur, V.P., Jampana, S.: An entropy-based evaluation method for knowledge bases of medical information systems. Expert. Syst. Appl. 46, 262\u2013273 (2016)","journal-title":"Expert Syst. Appl."},{"issue":"1","key":"1198_CR25","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/s11277-014-1748-5","volume":"78","author":"SD Xie","year":"2014","unstructured":"Xie, S.D., Wang, Y.X.: Construction of tree network with limited delivery latency in homogeneous wireless sensor networks. Wirel. Pers. Commun. 78(1), 231\u2013246 (2014)","journal-title":"Wireless Pers. Commun."},{"key":"1198_CR26","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","volume":"27","author":"C Shannon","year":"1948","unstructured":"Shannon, C.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379\u2013423 (1948)","journal-title":"Bell Syst. Tech. J."},{"key":"1198_CR27","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1080\/03081079908935239","volume":"28","author":"MJ Wierman","year":"1999","unstructured":"Wierman, M.J.: Measuring uncertainty in rough set theory. Int. J. Gen. Syst. 28, 283\u2013297 (1999)","journal-title":"Int. J. Gen Syst"},{"key":"1198_CR28","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1080\/03081070600687668","volume":"35","author":"JY Liang","year":"2006","unstructured":"Liang, J.Y., Shi, Z.Z., Li, D.Y., Wierman, M.J.: The information entropy, rough entropy and knowledge granulation in incomplete information systems. Int. J. Gen. Syst. 35, 641\u2013654 (2006)","journal-title":"Int. J. Gen Syst"},{"key":"1198_CR29","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.ins.2013.03.045","volume":"240","author":"JH Dai","year":"2013","unstructured":"Dai, J.H., Tian, H.W.: Entropy measures and granularity measures for set-valued information systems. Inf. Sci. 240, 72\u201382 (2013)","journal-title":"Inf. Sci."},{"issue":"2","key":"1198_CR30","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1109\/TFUZZ.2010.2095461","volume":"19","author":"YH Qian","year":"2011","unstructured":"Qian, Y.H., Liang, J.Y., Wu, W.Z., Dang, C.Y.: Information granularity in fuzzy binary GrC model. IEEE Trans. Fuzzy Syst. 19(2), 253\u2013264 (2011)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1198_CR31","first-page":"2338","volume":"27","author":"ZW Li","year":"2019","unstructured":"Li, Z.W., Zhang, P.F., Ge, X., Xie, N.X., Zhang, G.Q., Wen, C.F.: Uncertainty measurement for a fuzzy relation information system. IEEE Trans. Fuzzy Syst. 27, 2338\u20132352 (2019)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1198_CR32","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.ins.2018.08.047","volume":"470","author":"NX Xie","year":"2019","unstructured":"Xie, N.X., Liu, M., Li, Z.W., Zhang, G.Q.: New measures of uncertainty for an interval-valued information system. Inf. Sci. 470, 156\u2013174 (2019)","journal-title":"Inf. Sci."},{"key":"1198_CR33","volume":"196","author":"ZW Li","year":"2020","unstructured":"Li, Z.W., Liu, X.F., Dai, J.H., Chen, J.L., Fujita, H.: Measures of uncertainty based on Gaussian kernel for a fully fuzzy information system. Knowl.-Based Syst. 196, 105791 (2020)","journal-title":"Knowl.-Based Syst."},{"key":"1198_CR34","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2020.3041588","author":"J Cheng","year":"2020","unstructured":"Cheng, J., Huang, W., Lam, H.K., Cao, J., Zhang, Y.: Fuzzy-model-based control for singularly perturbed systems with nonhomogeneous Markov switching: a dropout compensation strategy. IEEE Trans. Fuzzy Syst. (2020). https:\/\/doi.org\/10.1109\/TFUZZ.2020.3041588","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1198_CR35","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2020.2974440","author":"J Cheng","year":"2020","unstructured":"Cheng, J., Shan, Y., Cao, J., Park, J.H.: Nonstationary control for T-S fuzzy Markovian switching systems with variable quantization density. IEEE Trans. Fuzzy Syst. (2020). https:\/\/doi.org\/10.1109\/TFUZZ.2020.2974440","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1198_CR36","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.ijar.2019.08.009","volume":"114","author":"NX Xie","year":"2019","unstructured":"Xie, N.X., Li, Z.W., Wu, W.Z., Zhang, G.Q.: Fuzzy information granular structures: a further investigation. Int. J. Approx. Reason. 114, 127\u2013150 (2019)","journal-title":"Int. J. Approximate Reasoning"},{"issue":"6","key":"1198_CR37","doi-asserted-by":"crossref","first-page":"2245","DOI":"10.1109\/TFUZZ.2015.2417893","volume":"23","author":"YH Qian","year":"2015","unstructured":"Qian, Y.H., Li, Y., Liang, J.Y., Lin, G.P., Dang, C.Y.: Fuzzy granular structure distance. IEEE Trans. Fuzzy Syst. 23(6), 2245\u20132259 (2015)","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"1198_CR38","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.fss.2018.07.006","volume":"360","author":"CZ Wang","year":"2019","unstructured":"Wang, C.Z., Huang, Y., Shao, M.W., Chen, D.G.: Uncertainty measures for general fuzzy relations. Fuzzy Sets Syst. 360, 82\u201396 (2019)","journal-title":"Fuzzy Sets Syst."},{"key":"1198_CR39","volume-title":"Algebra","author":"TW Hungerford","year":"1974","unstructured":"Hungerford, T.W.: Algebra. Springer, New York (1974)"},{"key":"1198_CR40","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-9333-5","volume-title":"Semirings and their applications","author":"JS Golan","year":"1999","unstructured":"Golan, J.S.: Semirings and Their Applications. Kluwer Academic Publishers, Dordrecht (1999)"},{"key":"1198_CR41","first-page":"1","volume":"7","author":"J Dem\u0161ar","year":"2006","unstructured":"Dem\u0161ar, J.: Statistical comparisons of classifiers over multiple data sets. J. Mach. Learn. Res. 7, 1\u201330 (2006)","journal-title":"J. Mach. Learn. Res."},{"issue":"12","key":"1198_CR42","first-page":"2677","volume":"9","author":"G Salvador","year":"2008","unstructured":"Salvador, G., Herrera, F.: An extension on \u201cstatistical comparisons of classifiers over multiple data sets\u201d for all pairwise comparisons. J. Mach. Learn. Res. 9(12), 2677\u20132694 (2008)","journal-title":"J. Mach. Learn. Res."},{"issue":"293","key":"1198_CR43","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1080\/01621459.1961.10482090","volume":"56","author":"OJ Dunn","year":"1961","unstructured":"Dunn, O.J.: Multiple comparisons among means. J. Am. Stat. Assoc. 56(293), 52\u201364 (1961)","journal-title":"J. Am. Stat. Assoc."},{"issue":"1","key":"1198_CR44","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1214\/aoms\/1177731944","volume":"11","author":"M Friedman","year":"1940","unstructured":"Friedman, M.: A comparison of alternative tests of significance for the problem of m rankings. Ann. Math. Stat. 11(1), 86\u201392 (1940)","journal-title":"Ann. Math. Stat."}],"container-title":["International Journal of Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-021-01198-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40815-021-01198-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40815-021-01198-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,4]],"date-time":"2022-05-04T16:27:44Z","timestamp":1651681664000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40815-021-01198-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,30]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["1198"],"URL":"https:\/\/doi.org\/10.1007\/s40815-021-01198-4","relation":{},"ISSN":["1562-2479","2199-3211"],"issn-type":[{"type":"print","value":"1562-2479"},{"type":"electronic","value":"2199-3211"}],"subject":[],"published":{"date-parts":[[2021,11,30]]},"assertion":[{"value":"17 April 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 July 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 November 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}