{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:47:43Z","timestamp":1777704463798,"version":"3.51.4"},"reference-count":15,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2018,9,7]],"date-time":"2018-09-07T00:00:00Z","timestamp":1536278400000},"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 & Fuzzy Systems"],"published-print":{"date-parts":[[2018,10,27]]},"abstract":"\n In this paper, our aim is to introduce and study some new spaces of lacunary\n \n \n I<\/mml:mi>\n <\/mml:math>\n <\/jats:inline-formula>\n - convergence for sequence of fuzzy real number which are defined by compact operator (\n T<\/jats:italic>\n ) on the real space\n \n \n \n \u211d<\/mml:mi>\n <\/mml:mstyle>\n <\/mml:math>\n <\/jats:inline-formula>\n . i.e.,\n \n \n \n \n c<\/mml:mi>\n \n F<\/mml:mi>\n \n <\/mml:mmultiscripts>\n \n \n \n \n I<\/mml:mi>\n \u03b8<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:msup>\n (<\/mml:mo>\n T<\/mml:mi>\n )<\/mml:mo>\n ,<\/mml:mo>\n \u2009<\/mml:mtext>\n \n c<\/mml:mi>\n \n F<\/mml:mi>\n \n <\/mml:mmultiscripts>\n \n \n 0<\/mml:mn>\n \n \n I<\/mml:mi>\n \u03b8<\/mml:mi>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:msubsup>\n (<\/mml:mo>\n T<\/mml:mi>\n )<\/mml:mo>\n ,<\/mml:mo>\n \u2009<\/mml:mtext>\n \n \u2113<\/mml:mi>\n \n F<\/mml:mi>\n \n <\/mml:mmultiscripts>\n \n \n \u221e<\/mml:mi>\n \n I<\/mml:mi>\n \u03b8<\/mml:mi>\n <\/mml:msub>\n <\/mml:msubsup>\n (<\/mml:mo>\n T<\/mml:mi>\n )<\/mml:mo>\n ,<\/mml:mo>\n \u2009<\/mml:mtext>\n \n \u2113<\/mml:mi>\n \n F<\/mml:mi>\n \n <\/mml:mmultiscripts>\n \n \n \u221e<\/mml:mi>\n \u03b8<\/mml:mi>\n <\/mml:msubsup>\n (<\/mml:mo>\n T<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and examine some basic properties and prove some inclusions relation on these spaces.\n <\/jats:p>","DOI":"10.3233\/jifs-18906","type":"journal-article","created":{"date-parts":[[2018,9,11]],"date-time":"2018-09-11T16:52:15Z","timestamp":1536684735000},"page":"4849-4855","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["On fuzzy valued lacunary ideal convergent sequence spaces defined by a compact operator"],"prefix":"10.1177","volume":"35","author":[{"given":"Vakeel A.","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh, India"}]},{"given":"Abdullah A.H.","family":"Makharesh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh, India"}]},{"given":"Kamal M.A.S","family":"Alshlool","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh, India"}]},{"given":"Sameera A.A.","family":"Abdullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh, India"}]},{"given":"Hira","family":"Fatima","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh, India"}]}],"member":"179","published-online":{"date-parts":[[2018,9,7]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.2140\/pjm.1993.160.43"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2011.09.037"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.21833\/ijaas.2017.04.007"},{"issue":"2","key":"e_1_3_2_5_2","first-page":"141","article-title":"On some i- convergent sequence spaces de ned by a compact operator","volume":"43","author":"Khan V.A.","year":"2016","unstructured":"KhanV.A., ShafiqM., RababahR.K.A. and EsiA., On some i- convergent sequence spaces de ned by a compact operator, Annals of the University of Craiova-Mathematics and Computer Science Series 43(2) (2016), 141\u2013150.","journal-title":"Annals of the University of Craiova-Mathematics and Computer Science Series"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.3923\/jas.2017.467.474"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/44154069"},{"key":"e_1_3_2_8_2","volume-title":"Introductory functional analysis with applications","author":"Kreyszig E.","year":"1978","unstructured":"KreyszigE. 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