{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T14:56:19Z","timestamp":1770476179507,"version":"3.49.0"},"reference-count":37,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2018,8,20]],"date-time":"2018-08-20T00:00:00Z","timestamp":1534723200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,10]]},"abstract":"<jats:p>In this paper, based on a type-2 fuzzy set, structures of fuzzy truth values on a linearly ordered set are investigated. Some special type-2 fuzzy sets are first presented. Then, rough approximations of fuzzy truth values based on a type-2 fuzzy set are introduced. Next, topological and rough structures of fuzzy truth values based on a type-2 fuzzy set are obtained. Finally, rough equal relations of fuzzy truth values based on a type-2 fuzzy set are proposed. These results will be helpful for the study of type-2 fuzzy sets.<\/jats:p>","DOI":"10.3233\/jifs-18082","type":"journal-article","created":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T15:54:54Z","timestamp":1534866894000},"page":"3553-3566","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Structures of fuzzy truth values based on a type-2 fuzzy set"],"prefix":"10.1177","volume":"35","author":[{"given":"Bin","family":"Qin","sequence":"first","affiliation":[{"name":"School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, Guangxi, P.R. China"}]}],"member":"179","published-online":{"date-parts":[[2018,8,20]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(68)90057-7"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019713018007"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1006582718102"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.05.002"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.04.005"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.5666\/KMJ.2014.54.3.413"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.5269\/bspm.v32i2.19868"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2013.07.023"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.07.011"},{"issue":"6","key":"e_1_3_2_11_2","first-page":"563","volume":"6","author":"John R.I.","year":"1998","unstructured":"R.I.John, Type-2 fuzzy sets: An appraisal of theory and applications, International Journal of Uncertainty, Fuzzi-ness and Knowledge-Based Systems 6(6) (1998), 563\u2013576.","journal-title":"Type-2 fuzzy sets: An appraisal of theory and applications, International Journal of Uncertainty, Fuzzi-ness and Knowledge-Based Systems"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(00)00079-8"},{"key":"e_1_3_2_13_2","first-page":"195","volume":"132","author":"Karnik N.N.","year":"2001","unstructured":"N.N.Karnik and J.M.Mendel, Centroid of a type-2 fuzzy set, Information Sciences 132 (2001), 195\u2013220.","journal-title":"Centroid of a type-2 fuzzy set, Information Sciences"},{"key":"e_1_3_2_14_2","volume-title":"Fuzzy topology","author":"Liu Y.M.","year":"1998","unstructured":"Y.M.Liu and M.K.Luo, Fuzzy topology, World Scientific Publishing, Singapore, 1998."},{"key":"e_1_3_2_15_2","volume-title":"Uncertain rule-based fuzzy logic systems: Introduction and new directions","author":"Mendel J.M.","year":"2001","unstructured":"J.M.Mendel, Uncertain rule-based fuzzy logic systems: Introduction and new directions, Prentice-Hall, Upper Saddle River, NJ, 2001."},{"key":"e_1_3_2_16_2","first-page":"84","volume":"177","author":"Mendel J.M.","year":"2007","unstructured":"J.M.Mendel, Advances in type-2 fuzzy sets and systems, Information Sciences 177 (2007), 84\u2013110.","journal-title":"Advances in type-2 fuzzy sets and systems, Information Sciences"},{"key":"e_1_3_2_17_2","first-page":"20","volume":"2","author":"Mendel J.M.","year":"2007","unstructured":"J.M.Mendel, Type-2 fuzzy sets and systems: An overview, IEEE Computation Intelligence Magazine 2 (2007), 20\u201329.","journal-title":"Type-2 fuzzy sets and systems: An overview, IEEE Computation Intelligence Magazine"},{"key":"e_1_3_2_18_2","first-page":"988","volume":"177","author":"Mendel J.M.","year":"2007","unstructured":"J.M.Mendel, Computing with words and its relationships with fuzzistics, Information Sciences 177 (2007), 988\u20131006.","journal-title":"Computing with words and its relationships with fuzzistics, Information Sciences"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1109\/91.995115"},{"issue":"6","key":"e_1_3_2_20_2","first-page":"808","volume":"14","author":"Mendel J.M.","year":"2006","unstructured":"J.M.Mendel, R.I.John and F.Liu, Interval type-2 fuzzy logic systems made simple, IEEE Transactions on Fuzzy Systems 14(6) (2006), 808\u2013821.","journal-title":"Interval type-2 fuzzy logic systems made simple, IEEE Transactions on Fuzzy Systems"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2006.889959"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.03.003"},{"key":"e_1_3_2_23_2","first-page":"261","article-title":"On the algebraic structure of fuzzy sets of type 2","volume":"13","author":"Nieminen J.","year":"1977","unstructured":"J.Nieminen, On the algebraic structure of fuzzy sets of type 2, Kybernetika 13 (1977), 261\u2013273.","journal-title":"Kybernetika"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-3534-4"},{"key":"e_1_3_2_26_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(80)90048-7"},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.06.003"},{"key":"e_1_3_2_28_2","first-page":"28","volume":"177","author":"Pawlak Z.","year":"2007","unstructured":"Z.Pawlak and A.Skowron, Rough sets: Some extensions, Information Sciences 177 (2007), 28\u201340.","journal-title":"Rough sets: Some extensions, Information Sciences"},{"key":"e_1_3_2_29_2","first-page":"41","volume":"177","author":"Pawlak Z.","year":"2007","unstructured":"Z.Pawlak and A.Skowron, Rough sets and Boolean reasoning, Information Sciences 177 (2007), 41\u201373.","journal-title":"Rough sets and Boolean reasoning, Information Sciences"},{"issue":"1","key":"e_1_3_2_30_2","first-page":"57","article-title":"On convergence of series of fuzzy real numbers","volume":"39","author":"Tripathy B.C.","year":"2012","unstructured":"B.C.Tripathy and P.C.Das, On convergence of series of fuzzy real numbers, Kuwait Journal of Science & Engineering 39(1A) (2012), 57\u201370.","journal-title":"Kuwait Journal of Science & Engineering"},{"key":"e_1_3_2_31_2","doi-asserted-by":"publisher","DOI":"10.5269\/bspm.v32i2.20896"},{"issue":"10","key":"e_1_3_2_32_2","first-page":"1691","volume":"16","author":"Tripathy B.C.","year":"2012","unstructured":"B.C.Tripathy and G.C.Ray, On Mixed fuzzy topological spaces and countability, Soft Computing 16(10) (2012), 1691\u20131695.","journal-title":"On Mixed fuzzy topological spaces and countability, Soft Computing"},{"issue":"2","key":"e_1_3_2_33_2","first-page":"331","volume":"36","author":"Tripathy B.C.","year":"2014","unstructured":"B.C.Tripathy and G.C.Ray, Weakly continuous functions on mixed fuzzy topological spaces, Acta Scientiarum-Technology 36(2) (2014), 331\u2013335.","journal-title":"Weakly continuous functions on mixed fuzzy topological spaces, Acta Scientiarum-Technology"},{"key":"e_1_3_2_34_2","first-page":"602","volume":"220","author":"Tripathy B.C.","year":"2013","unstructured":"B.C.Tripathy and G.C.Ray, Mixed fuzzy ideal topological spaces, Applied Mathematics and Computations 220 (2013), 602\u2013607.","journal-title":"Mixed fuzzy ideal topological spaces, Applied Mathematics and Computations"},{"key":"e_1_3_2_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2003.12.003"},{"key":"e_1_3_2_36_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_37_2","first-page":"199","volume":"8","author":"Zadeh L.A.","year":"1975","unstructured":"L.A.Zadeh, The concept of a linguistic variable and its application to approximate reasoning (I), Information Sciences 8 (1975), 199\u2013249.","journal-title":"The concept of a linguistic variable and its application to approximate reasoning (I), Information Sciences"},{"key":"e_1_3_2_38_2","volume-title":"Rough set theory and methods","author":"Zhang W.X.","year":"2001","unstructured":"W.X.Zhang, W.Z.Wu, J.Y.Liang and D.Y.Li, Rough set theory and methods, Chinese Scientific Publishers, Beijing, 2001."}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18082","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-18082","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-18082","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T19:27:29Z","timestamp":1770406049000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-18082"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8,20]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,10]]}},"alternative-id":["10.3233\/JIFS-18082"],"URL":"https:\/\/doi.org\/10.3233\/jifs-18082","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8,20]]}}}