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This paper investigates invariant characteristics of knowledge structures in a knowledge base under homomorphisms and their uncertainty measures. First, partial dependence knowledge structures in the same knowledge base is proposed and the concept of knowledge structure bases is presented. Then, invariant and inverse invariant characteristics of knowledge structures in a knowledge base under homomorphisms are obtained. Next, measuring uncertainty of knowledge structures in the same knowledge base is investigated. Finally, two examples are employed to illustrate that knowledge granulation, rough entropy, knowledge entropy and knowledge amount of knowledge structures, and knowledge distance between knowledge structures are neither invariant nor inverse invariant under homomorphisms, and third example shows the feasibility of the proposed measures for uncertainty of knowledge structures in the same knowledge base. These results will be helpful for building a skeleton of granular computing in knowledge bases.<\/jats:p>","DOI":"10.3233\/jifs-172048","type":"journal-article","created":{"date-parts":[[2018,7,24]],"date-time":"2018-07-24T17:27:17Z","timestamp":1532453237000},"page":"5689-5705","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Invariant characteristics of knowledge structures in a knowledge base under homomorphisms and their uncertainty measures"],"prefix":"10.1177","volume":"35","author":[{"given":"Sichun","family":"Wang","sequence":"first","affiliation":[{"name":"Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi University of Finance and Economics, Nanning, Guangxi, P.R.China"}]},{"given":"Fei","family":"Xia","sequence":"additional","affiliation":[{"name":"Guangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi University of Finance and Economics, Nanning, Guangxi, P.R.China"}]}],"member":"179","published-online":{"date-parts":[[2018,7,23]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(98)00019-X"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(98)00091-5"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.14311\/NNW.2016.26.035"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/1098-111X(200101)16:1<105::AID-INT8>3.0.CO;2-S"},{"key":"e_1_3_1_6_2","first-page":"39","article-title":"Rough set approach to incomplete information systems","volume":"112","author":"Kryszkiewicz M.","year":"1998","unstructured":"KryszkiewiczM., Rough set approach to incomplete information systems, International Sciences 112 (1998), 39\u201349.","journal-title":"International Sciences"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.01.014"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.11.011"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10115-015-0902-z"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1111\/exsy.12183"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2011.02.011"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.12.010"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2017.02.033"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(98)00021-6"},{"key":"e_1_3_1_15_2","first-page":"107","volume-title":"Rough Sets In Knowledge Discovery","author":"Lin T.Y.","year":"1998","unstructured":"LinT.Y., Granular computing on binary relations I: Data mining and neighborhood systems, In: Rough Sets In Knowledge Discovery, SkowronA. and PolkowskiL. 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