{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,12]],"date-time":"2024-07-12T15:20:43Z","timestamp":1720797643561},"reference-count":17,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Residuated lattices play an important role in the study of fuzzy logic based on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>t<\/mml:mi><\/mml:mrow><\/mml:math>-norms. In this paper, we introduce some notions of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>-fold filters in residuated lattices, study the relations among them, and compare them with prime, maximal and primary, filters. This work generalizes existing results in BL-algebras and residuated lattices, most notably the works of Lele et al., Motamed et al., Haveski et al., Borzooei et al., Van Gasse et al., Kondo et al., Turunen et al., and Borumand Saeid et al., we draw diagrams summarizing the relations between different types of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>-fold filters and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>-fold residuated lattices.<\/jats:p>","DOI":"10.1155\/2014\/428940","type":"journal-article","created":{"date-parts":[[2014,6,25]],"date-time":"2014-06-25T17:03:54Z","timestamp":1403715834000},"page":"1-12","source":"Crossref","is-referenced-by-count":11,"title":["Folding Theory Applied to Residuated Lattices"],"prefix":"10.1155","volume":"2014","author":[{"given":"Albert","family":"Kadji","sequence":"first","affiliation":[{"name":"Departmen of Mathematics, University of Yaounde 1, P.O. Box 812, Yaounde, Cameroon"}]},{"given":"Celestin","family":"Lele","sequence":"additional","affiliation":[{"name":"Departmen of Mathematics, University of Dschang, P.O. Box 67, Dschang, Cameroon"}]},{"given":"Jean B.","family":"Nganou","sequence":"additional","affiliation":[{"name":"Departmen of Mathematics, University of Oregon, Eugene, OR 97403, USA"}]},{"given":"Marcel","family":"Tonga","sequence":"additional","affiliation":[{"name":"Departmen of Mathematics, University of Yaounde 1, P.O. Box 812, Yaounde, Cameroon"}]}],"member":"98","reference":[{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5300-3"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200710029"},{"issue":"4","key":"14","doi-asserted-by":"crossref","first-page":"29","DOI":"10.4018\/jalr.2010100103","volume":"1","year":"2010","journal-title":"International Journal of Artificial Life Research"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-011-0548-z"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-31709-5_56"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-005-0534-4"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2010.04.010"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-007-0178-7"},{"issue":"4","key":"2","first-page":"413","volume":"55(103)","year":"2012","journal-title":"Bulletin Math\u00e9matique de la Soci\u00e9t\u00e9 des Sciences Math\u00e9matiques de Roumanie"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/s13370-013-0184-0"},{"key":"11","first-page":"33","volume":"1769","year":"2011","journal-title":"School of Information Environment"},{"issue":"6","key":"10","first-page":"839","volume":"29","year":"1984","journal-title":"Mathematica Japonica"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-012-0849-x"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/763428"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1017\/S144678870000851X"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2012.09.014"},{"key":"1","first-page":"70","volume":"7","year":"2009","journal-title":"World Applied Sciences Journal"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/428940.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/428940.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/428940.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T11:32:13Z","timestamp":1498131133000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2014\/428940\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":17,"alternative-id":["428940","428940"],"URL":"https:\/\/doi.org\/10.1155\/2014\/428940","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}