{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:19:17Z","timestamp":1746803957473,"version":"3.40.5"},"reference-count":41,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2018]]},"abstract":"<jats:p>We give in this paper the definitions of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>L<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-double fuzzy filter base and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>L<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-double fuzzy filter structures where <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>L<\/mml:mi><\/mml:mrow><\/mml:math> and <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>M<\/mml:mi><\/mml:mrow><\/mml:math> are strictly two-sided commutative quantales, and we also investigate the relations between them. Moreover, we propose second-order image and preimage operators of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>L<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-double fuzzy filter base and study some of its fundamental properties. Finally, we handle the given structures in the categorical aspect. For instance, we show that the category <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>L<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-<jats:bold>DFIL<\/jats:bold> of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>L<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-double fuzzy filter spaces and filter maps between these spaces is a topological category over the category<jats:bold> SET<\/jats:bold>.<\/jats:p>","DOI":"10.1155\/2018\/3871282","type":"journal-article","created":{"date-parts":[[2018,5,15]],"date-time":"2018-05-15T19:32:18Z","timestamp":1526412738000},"page":"1-15","source":"Crossref","is-referenced-by-count":1,"title":["On <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>L<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>M<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-Double Fuzzy Filter Spaces"],"prefix":"10.1155","volume":"2018","author":[{"given":"A. 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Box 3135, Alexandria, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Ayg\u00fcn","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kocaeli University, 41380 Kocaeli, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3136-0124","authenticated-orcid":true,"given":"V.","family":"\u00c7etkin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kocaeli University, 41380 Kocaeli, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"41","first-page":"89","volume":"11","year":"1985","journal-title":"Rendiconti del Circolo Matematico di Palermo, Serie II"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(68)90057-7"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2005.02.001"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.22436\/jnsa.006.04.04"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(80)90173-0"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5079-2_5"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1080\/16073606.1997.9632016"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(76)90029-9"},{"issue":"1","key":"35","first-page":"77","volume":"8","year":"2011","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"37","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-5079-2_6"},{"issue":"1","key":"40","first-page":"79","volume":"1","year":"2004","journal-title":"Iranian Journal of Fuzzy Systems"},{"key":"42","doi-asserted-by":"publisher","DOI":"10.1070\/RM1989v044n06ABEH002295"},{"key":"43","doi-asserted-by":"publisher","DOI":"10.1007\/BF02363065"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(86)80034-3"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00076-0"},{"key":"12","first-page":"67","volume":"67","year":"1996","journal-title":"Busefal"},{"key":"39","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(01)00235-4"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2005.05.023"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00262-5"},{"issue":"3","key":"6","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/S0165-0114(97)00261-3","volume":"106","year":"1999","journal-title":"Fuzzy Sets and Systems"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00058-S"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(95)00057-R"},{"year":"1995","key":"22"},{"year":"1997","key":"32"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.10.017"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.05.014"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/328153"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(94)00368-H"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(03)00129-5"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-1617-0"},{"key":"36","first-page":"99","volume":"12","year":"1986","journal-title":"Supplemento ai Rendiconti del Circolo Matematico di Palermo. 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