{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:25:35Z","timestamp":1777703135155,"version":"3.51.4"},"reference-count":46,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2015,8,10]],"date-time":"2015-08-10T00:00:00Z","timestamp":1439164800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2015,8,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Multi-level linear programming problem subject to addition-min fuzzy relation inequalities is introduced to characterize a kind of optimization models in BitTorrent-like Peer-to-Peer file sharing systems. Based on some theorems, which contribute to the resolution of the proposed problem, we develop a novel algorithm to find the unique optimal solution. A practical application example is presented to illustrate the feasibility and efficiency of the algorithm.<\/jats:p>","DOI":"10.3233\/ifs-151546","type":"journal-article","created":{"date-parts":[[2015,8,21]],"date-time":"2015-08-21T15:55:09Z","timestamp":1440172509000},"page":"2679-2689","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":29,"title":["Multi-level linear programming subject to addition-min fuzzy relation inequalities with application in Peer-to-Peer file sharing system"],"prefix":"10.1177","volume":"28","author":[{"given":"Xiao-Peng","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, China"},{"name":"Department of Mathematics and Statistics, Hanshan Normal University, Chaozhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xue-Gang","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, China"},{"name":"Department of Applied Mathematics, Guangdong University of Finance, Guangzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing-Yuan","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, China"},{"name":"Guangzhou Vocational College of Science and Technology, Guangzhou, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,8,10]]},"reference":[{"key":"e_1_3_1_2_1","unstructured":"SanchezE1972Th\u00e8se Biologie Humaine MarseilleEquations de Relations FlouesFrance"},{"key":"e_1_3_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(76)90446-0"},{"key":"e_1_3_1_4_1","unstructured":"SanchezE1977Solutions in composite fuzzy relation equations: Application to medical diagnosis in Brouwerian logicGuptaMMSaridisGNGainesRRFuzzy automata and decision processes221234North-HollandAmsterdam"},{"key":"e_1_3_1_5_1","unstructured":"DiNolaASessaSPedryczWSanchezE1989FuzzyRelationEquations and their Applications to KnowledgeEngineeringDordrecht Boston LondonAcademic Publishers"},{"key":"e_1_3_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2004.04.003"},{"key":"e_1_3_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2005.11.008"},{"key":"e_1_3_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2005.12.004"},{"key":"e_1_3_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2006.09.002"},{"key":"e_1_3_1_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.05.043"},{"key":"e_1_3_1_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.07.028"},{"key":"e_1_3_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(82)90043-4"},{"key":"e_1_3_1_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-011-9100-y"},{"key":"e_1_3_1_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4754(01)00387-1"},{"key":"e_1_3_1_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00104-3"},{"key":"e_1_3_1_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-001-0157-3"},{"key":"e_1_3_1_17_1","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2002.806322"},{"key":"e_1_3_1_18_1","first-page":"67","article-title":"How many lower solutions does a fuzzy relation equation have?","volume":"18","author":"Wang PZ","year":"1984","unstructured":"WangPZSessaSDi NolaAPedryczW1984How many lower solutions does a fuzzy relation equation have?BUSEFAL186774","journal-title":"BUSEFAL"},{"key":"e_1_3_1_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2007.07.017"},{"key":"e_1_3_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(91)90222-L"},{"key":"e_1_3_1_21_1","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2009.2031561"},{"key":"e_1_3_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(97)00184-X"},{"key":"e_1_3_1_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00417-5"},{"key":"e_1_3_1_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2008.04.004"},{"key":"e_1_3_1_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.04.042"},{"key":"e_1_3_1_26_1","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2002.800657"},{"key":"e_1_3_1_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.12.027"},{"key":"e_1_3_1_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2004.09.010"},{"key":"e_1_3_1_29_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-005-4914-0"},{"key":"e_1_3_1_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.09.030"},{"key":"e_1_3_1_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2010.10.024"},{"key":"e_1_3_1_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00471-0"},{"key":"e_1_3_1_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2007.11.011"},{"key":"e_1_3_1_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2012.03.002"},{"key":"e_1_3_1_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2009.12.014"},{"key":"e_1_3_1_36_1","doi-asserted-by":"publisher","DOI":"10.1109\/FUZZY.2005.1452454"},{"key":"e_1_3_1_37_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10700-007-9017-7"},{"key":"e_1_3_1_38_1","unstructured":"CaoB-Y2002Fuzzy geometric programmingKluwer Academic PublishersBoston"},{"key":"e_1_3_1_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2012.04.037"},{"key":"e_1_3_1_40_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2008.04.007"},{"key":"e_1_3_1_41_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-009-9146-x"},{"key":"e_1_3_1_42_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2007.07.022"},{"key":"e_1_3_1_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.01.006"},{"key":"e_1_3_1_44_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2011.09.012"},{"key":"e_1_3_1_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cie.2014.03.024"},{"key":"e_1_3_1_46_1","doi-asserted-by":"publisher","DOI":"10.1109\/FSKD.2012.6233956"},{"key":"e_1_3_1_47_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2014.04.007"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151546","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/IFS-151546","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/IFS-151546","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:37:58Z","timestamp":1777455478000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/IFS-151546"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8,10]]},"references-count":46,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2015,8,10]]}},"alternative-id":["10.3233\/IFS-151546"],"URL":"https:\/\/doi.org\/10.3233\/ifs-151546","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8,10]]}}}