{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T04:56:23Z","timestamp":1764996983721},"reference-count":24,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Scientific Research Program Funded by Shaanxi Provincial Education Department","award":["12JK0878"],"award-info":[{"award-number":["12JK0878"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>By means of the function induced by a logical formula<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:math>, the concept of truth degree of the logical formula<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:math>is introduced in the 3-valued pre-rough logic in this paper. Moreover, similarity degrees among formulas are proposed and a pseudometric is defined on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in 3-value logic pre-rough logic is established.<\/jats:p>","DOI":"10.1155\/2013\/592738","type":"journal-article","created":{"date-parts":[[2013,6,24]],"date-time":"2013-06-24T21:01:06Z","timestamp":1372107666000},"page":"1-7","source":"Crossref","is-referenced-by-count":1,"title":["Truth Degrees Theory and Approximate Reasoning in 3-Valued Propositional Pre-Rough Logic"],"prefix":"10.1155","volume":"2013","author":[{"given":"Yingcang","family":"Ma","sequence":"first","affiliation":[{"name":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China"}]},{"given":"Juanjuan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China"}]},{"given":"Huan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Science, Xi\u2019an Polytechnic University, Xi\u2019an 710048, China"}]}],"member":"98","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01001956"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2008.04.005"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2007.05.001"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2007.03.016"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2007.08.008"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2007.05.019"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2008.06.004"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2010.11.019"},{"issue":"5-6","key":"9","first-page":"253","volume":"35","year":"1987","journal-title":"Bulletin of the Polish Academy of Sciences"},{"issue":"3-4","key":"10","first-page":"211","volume":"28","year":"1996","journal-title":"Fundamenta Informaticae"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(96)00334-9"},{"issue":"4","key":"12","first-page":"299","volume":"41","year":"1993","journal-title":"Polish Academy of Sciences"},{"issue":"2-3","key":"13","first-page":"139","volume":"71","year":"2006","journal-title":"Fundamenta Informaticae"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-71200-8_1"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/BF00935602"},{"issue":"1","key":"16","doi-asserted-by":"crossref","first-page":"61","DOI":"10.3233\/FI-1991-15105","volume":"15","year":"1991","journal-title":"Fundamenta Informaticae"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.3969\/j.issn.1001-0548.2011.02.028"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.09.008"},{"issue":"9","key":"19","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1360\/02ys9122","volume":"45","year":"2002","journal-title":"Science in China A"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/s11432-006-2001-y"},{"issue":"2","key":"21","first-page":"217","volume":"34","year":"2011","journal-title":"Acta Mathematicae Applicatae Sinica"},{"issue":"1","key":"22","first-page":"142","volume":"33","year":"2010","journal-title":"Acta Mathematicae Applicatae Sinica"},{"issue":"2","key":"23","first-page":"1","volume":"37","year":"2009","journal-title":"Journal of Shaanxi Normal University"},{"issue":"1","key":"24","doi-asserted-by":"crossref","first-page":"67","DOI":"10.3233\/FI-2011-393","volume":"107","year":"2011","journal-title":"Fundamenta Informaticae"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/592738.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/592738.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/592738.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,12]],"date-time":"2024-05-12T22:21:01Z","timestamp":1715552461000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/592738\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":24,"alternative-id":["592738","592738"],"URL":"https:\/\/doi.org\/10.1155\/2013\/592738","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}