{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T07:47:18Z","timestamp":1770277638036,"version":"3.49.0"},"reference-count":18,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2019,6,24]],"date-time":"2019-06-24T00:00:00Z","timestamp":1561334400000},"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":[[2019,11,22]]},"abstract":"<jats:p>\n                    Backward uncertain differential equation is a specical type of differential equation driven by a Liu process. There are some concepts of stability such as stability in measure, stability in mean, stability in\n                    <jats:italic>p<\/jats:italic>\n                    -th moment, stability moment exponential and almost sure stability of backward uncertain differential equations have been proposed. As a supplement, this paper gives a concept of stability in uncertain distribution of backward uncertain differential equation. Some sufficient conditions for a backward uncertain differential equation being stable in uncertain distribution are provided. In addition, this paper further discusses their relationships among stability in uncertain distribution, stability in uncertain measure, stability in mean and stability in\n                    <jats:italic>p<\/jats:italic>\n                    -th moment. Last, this paper discusses some examples to illustrate the theoretical considerations.\n                  <\/jats:p>","DOI":"10.3233\/jifs-182877","type":"journal-article","created":{"date-parts":[[2019,6,25]],"date-time":"2019-06-25T12:43:03Z","timestamp":1561466583000},"page":"7103-7110","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Stability in uncertain distribution for backward uncertain differential equation"],"prefix":"10.1177","volume":"37","author":[{"given":"Gang","family":"Shi","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Xinjiang University, Urumqi, China"}]},{"given":"Yuhong","family":"Sheng","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Xinjiang University, Urumqi, China"}]}],"member":"179","published-online":{"date-parts":[[2019,6,24]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-010-9073-2"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1186\/2195-5468-1-3"},{"issue":"3","key":"e_1_3_2_4_2","first-page":"223","article-title":"Existence and uniqueness theorem on uncertain differential equations with local Lipschitz condition","volume":"6","author":"Gao Y.","year":"2012","unstructured":"Y.Gao, Existence and uniqueness theorem on uncertain differential equations with local Lipschitz condition, J Uncertain Syst 6 (3) (2012), 223\u2013232.","journal-title":"J Uncertain Syst"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9147-4"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-73165-8_5"},{"issue":"1","key":"e_1_3_2_7_2","first-page":"3","article-title":"Fuzzy process, hybrid process and uncertain process","volume":"2","author":"Liu B.","year":"2008","unstructured":"B.Liu, Fuzzy process, hybrid process and uncertain process, J Uncertain Syst 2 (1) (2008), 3\u201316.","journal-title":"J Uncertain Syst"},{"issue":"1","key":"e_1_3_2_8_2","first-page":"3","article-title":"Some research problems in uncertainty theory","volume":"3","author":"Liu B.","year":"2009","unstructured":"B.Liu, Some research problems in uncertainty theory, J Uncertain Syst 3 (1) (2009), 3\u201310.","journal-title":"J Uncertain Syst"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-13959-8"},{"issue":"4","key":"e_1_3_2_10_2","first-page":"250","article-title":"Uncertain integral with respect to multiple canonical processes","volume":"6","author":"Liu B.","year":"2012","unstructured":"B.Liu and K.Yao, Uncertain integral with respect to multiple canonical processes, J Uncertain Syst 6 (4) (2012), 250\u2013255.","journal-title":"J Uncertain Syst"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-014-9188-y"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-130812"},{"issue":"9","key":"e_1_3_2_13_2","first-page":"3673","article-title":"Exponential stability for uncertain differential equation","volume":"20","author":"Sheng Y.","year":"2016","unstructured":"Y.Sheng and J.Gao, Exponential stability for uncertain differential equation, SoftComput 20 (9) (2016), 3673\u20133678.","journal-title":"SoftComput"},{"key":"e_1_3_2_14_2","article-title":"Stability analysis of backward uncertain differential equations","author":"Wang X.","unstructured":"X.Wang and Y.Ning, Stability analysis of backward uncertain differential equations, Technical Report.","journal-title":"Technical Report"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-17319"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-120688"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-012-9139-4"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-014-9204-2"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.3233\/JIFS-161661"}],"container-title":["Journal of Intelligent &amp; 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