{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T15:09:09Z","timestamp":1746803349618,"version":"3.40.5"},"reference-count":10,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100003824","name":"Hunan University","doi-asserted-by":"publisher","award":["10XKYTB038"],"award-info":[{"award-number":["10XKYTB038"]}],"id":[{"id":"10.13039\/501100003824","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>The purpose of this paper is to study theory of two different kinds of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><\/mml:math>-layer order-preserving operator space, namely,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msub><mml:mi>\u03c9<\/mml:mi><mml:mi>\u03b1<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>-<jats:italic>opos<\/jats:italic>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:msubsup><mml:mrow><mml:mi>\u03c9<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>*<\/mml:mi><\/mml:mrow><\/mml:msubsup><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>\u2111<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-<jats:italic>opos<\/jats:italic>. The former kind of space is formed by<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><\/mml:math>-layer function in<jats:italic>L<\/jats:italic>-fuzzy order-preserving operator space. The later kind of space is derived by local<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><\/mml:math>-remote neighborhood function, which is related with<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:msub><mml:mi>\u03c9<\/mml:mi><mml:mi>\u03b1<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>-<jats:italic>opos<\/jats:italic>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><\/mml:math>-ideal. We study characteristic properties of the two kinds of spaces, respectively, and give some applications to show the intimate relations under two different<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:msubsup><mml:mrow><mml:mi>\u03c9<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>\u03b1<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>*<\/mml:mi><\/mml:mrow><\/mml:msubsup><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>\u2111<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-<jats:italic>oposs<\/jats:italic>.<\/jats:p>","DOI":"10.1155\/2012\/582105","type":"journal-article","created":{"date-parts":[[2012,8,29]],"date-time":"2012-08-29T17:02:05Z","timestamp":1346259725000},"page":"1-8","source":"Crossref","is-referenced-by-count":0,"title":["On<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi mathvariant=\"bold-italic\">\u03b1<\/mml:mi><\/mml:mrow><\/mml:math>-Layer Ideal Topologies"],"prefix":"10.1155","volume":"2012","author":[{"given":"Xiu-Yun","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Institute of Computational Mathematics, Hunan University of Science and Engineering, Yongzhong 425100, China"}]},{"given":"Li-Li","family":"Xie","sequence":"additional","affiliation":[{"name":"Department of English Teaching, Hunan University of Science and Engineering, Yongzhong 425100, China"}]}],"member":"311","reference":[{"year":"1960","key":"9"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.2307\/2324512"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1023\/B:AMHU.0000024685.84429.e9"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-005-0210-2"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-005-0202-2"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(80)90048-7"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00032-2"},{"year":"1988","key":"11"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-008-9043-0"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/925948"}],"container-title":["Advances in Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2012\/582105.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2012\/582105.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/afs\/2012\/582105.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,2]],"date-time":"2016-08-02T17:15:26Z","timestamp":1470158126000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/afs\/2012\/582105\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":10,"alternative-id":["582105","582105"],"URL":"https:\/\/doi.org\/10.1155\/2012\/582105","relation":{},"ISSN":["1687-7101","1687-711X"],"issn-type":[{"type":"print","value":"1687-7101"},{"type":"electronic","value":"1687-711X"}],"subject":[],"published":{"date-parts":[[2012]]}}}