{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:46:30Z","timestamp":1777704390597,"version":"3.51.4"},"reference-count":32,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2020,4,30]],"date-time":"2020-04-30T00:00:00Z","timestamp":1588204800000},"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":[[2020,4,30]]},"abstract":"<jats:p>\n                    \u00a0As a key theoretical basis of fuzzy analysis, a new representation of the two-dimension fuzzy numbers is proposed in this paper. We also present a new method for solving the fuzzy system of linear equations with the two-dimension fuzzy data based on the new representation of the two-dimension fuzzy numbers, which may translate a fuzzy system of linear equations into two real systems of linear equations, one is an\n                    <jats:italic>n<\/jats:italic>\n                    \u00a0\u00d7\u00a0\n                    <jats:italic>n<\/jats:italic>\n                    real system of linear equations and the other is a (2\n                    <jats:italic>n<\/jats:italic>\n                    )\u00a0\u00d7\u00a0(2\n                    <jats:italic>n<\/jats:italic>\n                    ) real system of linear equations, where the coefficients, the right hand term and the unknown term of the (2\n                    <jats:italic>n<\/jats:italic>\n                    )\u00a0\u00d7\u00a0(2\n                    <jats:italic>n<\/jats:italic>\n                    ) real systems are all positive real numbers. Accordingly, we compare the classical methods with the technique on the basis of the study of the two-dimensional fuzzy linear system proposed in this paper for an one-dimensional fuzzy linear system, and the results shows that they have the same solutions. Finally, the conditions of the existence of the solutions for a fuzzy system of linear equations are discussed, and the examples are given to show the efficiency and effectiveness of the method investigated in this article.\n                  <\/jats:p>","DOI":"10.3233\/jifs-191927","type":"journal-article","created":{"date-parts":[[2020,5,1]],"date-time":"2020-05-01T13:31:20Z","timestamp":1588339880000},"page":"5295-5315","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Fuzzy linear systems with the two-dimension fuzzy data"],"prefix":"10.1177","volume":"38","author":[{"given":"Zhiyong","family":"Xiao","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou, PR China"},{"name":"School of Mathematics and Statistics, Longdong University, Qingyang, Gansu, PR China"}]},{"given":"Zengtai","family":"Gong","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Northwest Normal University, Lanzhou, PR China"}]},{"given":"Kun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Longdong University, Qingyang, Gansu, PR China"}]}],"member":"179","published-online":{"date-parts":[[2020,4,30]]},"reference":[{"key":"e_1_3_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.01.110"},{"key":"e_1_3_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.02.018"},{"key":"e_1_3_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.07.036"},{"key":"e_1_3_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00793-8"},{"key":"e_1_3_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.12.085"},{"key":"e_1_3_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.02.020"},{"key":"e_1_3_1_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.08.047"},{"key":"e_1_3_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2010.02.042"},{"key":"e_1_3_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-012-0858-9"},{"key":"e_1_3_1_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2012.01.002"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2011.02.010"},{"key":"e_1_3_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.07.048"},{"key":"e_1_3_1_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-012-0801-0"},{"key":"e_1_3_1_15_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10598-012-9152-z"},{"key":"e_1_3_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2014.02.014"},{"key":"e_1_3_1_17_2","first-page":"648","article-title":"Solution of fuzzy system of linear equations with polynomial parametric form","volume":"7","author":"Behera D.","year":"2012","unstructured":"BeheraD. and ChakravertyS., Solution of fuzzy system of linear equations with polynomial parametric form, Applications and Applied Mathematics An International Journal 7 (2012), 648\u2013657.","journal-title":"Applications and Applied Mathematics An International Journal"},{"key":"e_1_3_1_18_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12190-018-1204-x"},{"key":"e_1_3_1_19_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-2012-0627"},{"key":"e_1_3_1_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.07.033"},{"key":"e_1_3_1_21_2","article-title":"Metric spaces of fuzzy sets: theory and applications","author":"Diamond P.","year":"1994","unstructured":"DiamondP. and KloedenP.E., Metric spaces of fuzzy sets: theory and applications, World Scientific, 1994.","journal-title":"World Scientific"},{"key":"e_1_3_1_22_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-009-0537-7"},{"key":"e_1_3_1_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(96)00270-9"},{"key":"e_1_3_1_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(86)90026-6"},{"key":"e_1_3_1_25_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2017.03.029"},{"key":"e_1_3_1_26_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1116\/2\/022011"},{"key":"e_1_3_1_27_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(87)90029-7"},{"key":"e_1_3_1_28_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-5921-9"},{"key":"e_1_3_1_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2010.07.018"},{"key":"e_1_3_1_30_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2005.08.005"},{"key":"e_1_3_1_31_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(98)00284-X"},{"key":"e_1_3_1_32_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(91)90030-T"},{"key":"e_1_3_1_33_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10598-009-9039-9"}],"container-title":["Journal of Intelligent &amp; 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