{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T23:04:05Z","timestamp":1766012645753,"version":"3.41.2"},"reference-count":53,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T00:00:00Z","timestamp":1618185600000},"content-version":"vor","delay-in-days":101,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771263","11671007","61976130"],"award-info":[{"award-number":["11771263","11671007","61976130"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100009103","name":"Education Department of Shaanxi Province","doi-asserted-by":"publisher","award":["18JK0360"],"award-info":[{"award-number":["18JK0360"]}],"id":[{"id":"10.13039\/501100009103","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008049","name":"Xi'an Polytechnic University","doi-asserted-by":"publisher","award":["BS1426"],"award-info":[{"award-number":["BS1426"]}],"id":[{"id":"10.13039\/501100008049","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Following the idea of <jats:italic>L<\/jats:italic>\u2010fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join\u2010complete lattice structures of lower and upper approximation operators based on <jats:italic>L<\/jats:italic>\u2010fuzzy generalized neighborhood systems. In particular, as special approximation operators based on <jats:italic>L<\/jats:italic>\u2010fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on <jats:italic>L<\/jats:italic>\u2010fuzzy relations. Furthermore, if <jats:italic>L<\/jats:italic> satisfies the double negative law, then there exists an order isomorphic mapping between upper and lower approximation operators based on <jats:italic>L<\/jats:italic>\u2010fuzzy generalized neighborhood systems; when <jats:italic>L<\/jats:italic>\u2010fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on <jats:italic>L<\/jats:italic>\u2010fuzzy relations are complete lattice isomorphism.<\/jats:p>","DOI":"10.1155\/2021\/5523822","type":"journal-article","created":{"date-parts":[[2021,4,12]],"date-time":"2021-04-12T23:51:47Z","timestamp":1618271507000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["The Lattice Structures of Approximation Operators Based on L\u2010Fuzzy Generalized Neighborhood Systems"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8585-3170","authenticated-orcid":false,"given":"Qiao-Ling","family":"Song","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3094-1210","authenticated-orcid":false,"given":"Hu","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1100-6312","authenticated-orcid":false,"given":"Juan-Juan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3801-5318","authenticated-orcid":false,"given":"A. A.","family":"Ramadan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5909-4502","authenticated-orcid":false,"given":"Hong-Ying","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6590-791X","authenticated-orcid":false,"given":"Gui-Xiu","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2021,4,12]]},"reference":[{"key":"e_1_2_9_1_2","doi-asserted-by":"publisher","DOI":"10.1007\/bf01001956"},{"key":"e_1_2_9_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0165-0114(85)80029-4"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2009.12.003"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.03.009"},{"key":"e_1_2_9_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2011.05.001"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2018.05.023"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.06.021"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2003.08.005"},{"key":"e_1_2_9_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/tfuzz.2004.841734"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2003.11.003"},{"volume-title":"Neighborhoods, Rough Sets and Query Relaxation in Cooperative Answering,\u201d Rough Sets and Data Mining: Analysis of Imprecise Data","year":"1997","author":"Michael J. B.","key":"e_1_2_9_11_2"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/s0020-0255(02)00379-1"},{"key":"e_1_2_9_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2005.01.012"},{"key":"e_1_2_9_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.05.037"},{"key":"e_1_2_9_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.11.013"},{"key":"e_1_2_9_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.02.065"},{"key":"e_1_2_9_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2015.05.023"},{"key":"e_1_2_9_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.06.009"},{"key":"e_1_2_9_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.09.015"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-002-0165-y"},{"key":"e_1_2_9_21_2","first-page":"175","article-title":"Quantale-valued fuzzy scott topology","volume":"16","author":"Han S. E.","year":"2019","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_2_9_22_2","doi-asserted-by":"publisher","DOI":"10.3233\/jifs-151910"},{"key":"e_1_2_9_23_2","doi-asserted-by":"publisher","DOI":"10.3233\/jifs-18241"},{"key":"e_1_2_9_24_2","doi-asserted-by":"publisher","DOI":"10.2989\/16073606.2018.1441920"},{"key":"e_1_2_9_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2017.01.007"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.3390\/math7030228"},{"key":"e_1_2_9_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2010.10.002"},{"key":"e_1_2_9_28_2","doi-asserted-by":"publisher","DOI":"10.3233\/ifs-141522"},{"key":"e_1_2_9_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2016.02.014"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-018-3040-1"},{"volume-title":"\u201cTopological and Algebraic Structures in Fuzzy Sets,\u201d the Handbook of Recent Developments in the Mathematics of Fuzzy Sets","year":"2003","author":"Rodabaugh S. E.","key":"e_1_2_9_31_2"},{"key":"e_1_2_9_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.05.016"},{"key":"e_1_2_9_33_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081079.2017.1308360"},{"key":"e_1_2_9_34_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2008.01.006"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.06.029"},{"key":"e_1_2_9_36_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-27778-1_14"},{"key":"e_1_2_9_37_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.03.100"},{"key":"e_1_2_9_38_2","doi-asserted-by":"publisher","DOI":"10.3934\/math.2020360"},{"key":"e_1_2_9_39_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247x(67)90189-8"},{"key":"e_1_2_9_40_2","first-page":"115","article-title":"L-fuzzy approximation spaces and L-fuzzy topological spaces","volume":"13","author":"Ramadan A. A.","year":"2016","journal-title":"International Journal of Fuzzy Systems"},{"key":"e_1_2_9_41_2","first-page":"73","article-title":"Categories of lattice-valued closure (interior) operators and Alexandroff L-fuzzy topologies","volume":"16","author":"Ramadan A. A.","year":"2019","journal-title":"International Journal of Fuzzy Systems"},{"key":"e_1_2_9_42_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.03.027"},{"key":"e_1_2_9_43_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.02.011"},{"key":"e_1_2_9_44_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2010.01.003"},{"key":"e_1_2_9_45_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.02.002"},{"key":"e_1_2_9_46_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2018.10.016"},{"key":"e_1_2_9_47_2","first-page":"132","article-title":"Neighborhood systems: a qualitative theory for fuzzy and rough sets","volume":"4","author":"Lin T. Y.","year":"1997","journal-title":"Advances in Machine Intelligence and Soft Computing"},{"key":"e_1_2_9_48_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2014.04.017"},{"key":"e_1_2_9_49_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-017-2957-0"},{"key":"e_1_2_9_50_2","first-page":"53","article-title":"Rough approximation operators based on quantale-valued fuzzy generalized neighborhood systems","volume":"16","author":"Zhao F. F.","year":"2019","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"e_1_2_9_51_2","doi-asserted-by":"publisher","DOI":"10.1080\/03081079.2016.1144601"},{"key":"e_1_2_9_52_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0633-1"},{"key":"e_1_2_9_53_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5300-3"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/5523822.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/5523822.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/5523822","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T21:28:06Z","timestamp":1723238886000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/5523822"}},"subtitle":[],"editor":[{"given":"Heng","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":53,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/5523822"],"URL":"https:\/\/doi.org\/10.1155\/2021\/5523822","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-02-09","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-03-13","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-04-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"5523822"}}