{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:22:18Z","timestamp":1777702938348,"version":"3.51.4"},"reference-count":30,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2019,4,11]],"date-time":"2019-04-11T00:00:00Z","timestamp":1554940800000},"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":[[2019,4,11]]},"abstract":"<jats:p>\n                    In this article we establish a relation between the solutions of complex fuzzy differential equations, with complex membership grades, and approximate solutions by applying the properties of level-wise continuity for (\n                    <jats:italic>\u03c2<\/jats:italic>\n                    ,\n                    <jats:italic>\u03d1<\/jats:italic>\n                    )-level sets. The notion of\n                    <jats:italic>H<\/jats:italic>\n                    -differentiability is generalized for (\n                    <jats:italic>\u03c2<\/jats:italic>\n                    ,\n                    <jats:italic>\u03d1<\/jats:italic>\n                    )-level sets in the space\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msup>\n                          <mml:mover accent=\"true\">\n                            <mml:mi>E<\/mml:mi>\n                            <mml:mo stretchy=\"true\">\u02c6<\/mml:mo>\n                          <\/mml:mover>\n                          <mml:mrow>\n                            <mml:mn>2<\/mml:mn>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:msup>\n                        <mml:mo>.<\/mml:mo>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    Results about the existence and uniqueness of the solutions of Cauchy problem for complex fuzzy differential equations are also included.\n                  <\/jats:p>","DOI":"10.3233\/jifs-181611","type":"journal-article","created":{"date-parts":[[2019,4,12]],"date-time":"2019-04-12T10:39:21Z","timestamp":1555065561000},"page":"3567-3577","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Existence and uniqueness of approximate solutions to Cauchy problem of complex fuzzy differential equations"],"prefix":"10.1177","volume":"36","author":[{"given":"Maliha","family":"Rashid","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan"}]},{"given":"Nayyar","family":"Mehmood","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan"},{"name":"Department of Mathematical Sciences, College of Science, UAE University, UAE"}]},{"given":"Sumbal","family":"Shaheen","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan"}]}],"member":"179","published-online":{"date-parts":[[2019,4,11]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-010-0659-y"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-011-0759-3"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.11.009"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1956.6.397"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1137\/0315040"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(89)90122-X"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0087685"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.1972.5408553"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.01.005"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1142\/2326"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(82)80001-8"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90029-7"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2013.11.001"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.02.020"},{"key":"e_1_3_2_16_2","author":"Lakshmikantham V.","year":"1969","unstructured":"V.Lakshmikantham and S.Leela, Differential and Integral Inequalities: Theory and Applications: Volume I: Ordinary Differential Equations. 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