{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T09:49:57Z","timestamp":1718185797705},"reference-count":14,"publisher":"Hindawi Limited","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\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>On the basis of the theory of a falling shadow which was first formulated by Wang (1985), the notion of falling -ideals in -algebras is introduced, and related properties are investigated. Characterizations of a falling -ideal are established. Relations among falling -ideals, falling -ideals, falling -ideals, falling -subalgebras, and falling<jats:italic>BCK<\/jats:italic>-ideals are discussed.<\/jats:p>","DOI":"10.1155\/2012\/693090","type":"journal-article","created":{"date-parts":[[2012,3,5]],"date-time":"2012-03-05T20:42:57Z","timestamp":1330980177000},"page":"1-10","source":"Crossref","is-referenced-by-count":1,"title":["The Theory of Falling Shadows Applied to -Ideals in -Algebras"],"prefix":"10.1155","volume":"2012","author":[{"given":"Young Bae","family":"Jun","sequence":"first","affiliation":[{"name":"Department of Mathematics Education (and RINS), Gyeongsang National University, Chinju 660-701, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sun Shin","family":"Ahn","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Dongguk University, Seoul 100-715, Republic of Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"1","volume-title":"Fuzzy sets as equivalence classes of random sets","year":"1982"},{"key":"12","volume-title":"Treating a fuzzy subset as a projectable random set","year":"1982"},{"key":"13","year":"1985"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1993.1114"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(93)90171-D"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5331"},{"issue":"1","key":"2","first-page":"125","volume":"8","year":"1980","journal-title":"Mathematics Seminar Notes"},{"issue":"1","key":"3","first-page":"1","volume":"23","year":"1978","journal-title":"Mathematica Japonica"},{"issue":"1","key":"8","first-page":"19","volume":"49","year":"1999","journal-title":"Mathematica Slovaca"},{"issue":"1","key":"6","first-page":"123","volume":"8","year":"2000","journal-title":"Journal of Fuzzy Mathematics"},{"issue":"3","key":"9","first-page":"243","volume":"49","year":"1999","journal-title":"Mathematica Slovaca"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026466720971"},{"key":"5","volume":"2010","year":"2010","journal-title":"International Journal of Mathematics and Mathematical Sciences"},{"key":"4","volume":"2011","year":"2011","journal-title":"Discrete Dynamics in Nature and Society"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/693090.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/693090.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/693090.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,3]],"date-time":"2016-08-03T03:57:54Z","timestamp":1470196674000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2012\/693090\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":14,"alternative-id":["693090","693090"],"URL":"https:\/\/doi.org\/10.1155\/2012\/693090","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"value":"0161-1712","type":"print"},{"value":"1687-0425","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012]]}}}