{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T18:32:29Z","timestamp":1770748349002,"version":"3.50.0"},"reference-count":23,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2015,6,23]],"date-time":"2015-06-23T00:00:00Z","timestamp":1435017600000},"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":[[2015,6,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    Ranking fuzzy numbers is a very important issue in fuzzy sets theory and applications. The methods for ranking fuzzy numbers have been extensively researched and used to solve many problems. Recently, Chen et\u00a0al. [\n                    <jats:xref ref-type=\"bibr\">11<\/jats:xref>\n                    ] proposed a fuzzy ranking method to calculate the areas on the negative side, the areas on the positive side and the centroid of the generalized fuzzy numbers to evaluate the ranking scores of generalized fuzzy numbers with different left heights and right heights. The method can provide us with a useful way for fuzzy risk analysis based on generalized fuzzy numbers with different left heights and right heights. However, in several situations, the ranking results of Chen et\u00a0al.\u2019s method are unreasonable. In this paper, we propose an improved method, which considers the areas of the positive side, the areas of the negative side and the spreads of generalized fuzzy numbers as the ranking factors for ranking fuzzy numbers. The proposed method not only can rank generalized fuzzy numbers with different left heights and right heights, but also overcome the drawbacks of the existing fuzzy ranking methods.\n                  <\/jats:p>","DOI":"10.3233\/ifs-151639","type":"journal-article","created":{"date-parts":[[2015,7,1]],"date-time":"2015-07-01T11:37:59Z","timestamp":1435750679000},"page":"2343-2355","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":67,"title":["An improved method to rank generalized fuzzy numbers with different left heights and right heights"],"prefix":"10.1177","volume":"28","author":[{"given":"Wen","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an, China"}]},{"given":"Yu","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an, China"}]},{"given":"Xi-Yun","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an, China"}]},{"given":"Jun","family":"Zhan","sequence":"additional","affiliation":[{"name":"School of Electronics and Information, Northwestern Polytechnical University, Xi\u2019an, China"}]}],"member":"179","published-online":{"date-parts":[[2015,6,23]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177698950"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2010.07.004"},{"key":"e_1_3_2_5_2","doi-asserted-by":"crossref","unstructured":"SuXYMahadevanSXuPDDengYDependence assessment in Human Reliability Analysis using evidence theory and AHP Risk Analysis In Press2015","DOI":"10.1111\/risa.12347"},{"key":"e_1_3_2_6_2","first-page":"698","article-title":"Decisionmaking in the presence of fuzzy variables","volume":"6","author":"Jain R","year":"1976","unstructured":"JainR1976Decisionmaking in the presence of fuzzy variablesIEEE Trans Syst Man Cybern6698703","journal-title":"IEEE Trans Syst Man Cybern"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1080\/01969720302866"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.asoc.2011.11.011"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2002.806316"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-006-0003-5"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2008.08.015"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2011.12.004"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2010.08.002"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-2012-0628"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2008.06.112"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.10.090"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1080\/00207540903117873"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2007.05.009"},{"key":"e_1_3_2_19_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.07.064"},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2011.07.060"},{"key":"e_1_3_2_21_2","article-title":"Fuzzy risk analysis based on the novel fuzzy ranking with new arithmetic operations of linguistic fuzzy numbers,\u2013","volume":"26","author":"Madhuri KU","unstructured":"MadhuriKUBabuSSShankarNR2401Fuzzy risk analysis based on the novel fuzzy ranking with new arithmetic operations of linguistic fuzzy numbers,\u2013Journal of Intelligent & Fuzzy Systems26","journal-title":"Journal of Intelligent & Fuzzy Systems"},{"key":"e_1_3_2_22_2","doi-asserted-by":"publisher","DOI":"10.3233\/IFS-131082"},{"key":"e_1_3_2_23_2","first-page":"586","article-title":"Ranking triangle and trapezoidal fuzzy numbers based on the relative preference relation","volume":"39","author":"Wang YJ","year":"2015","unstructured":"WangYJ2015Ranking triangle and trapezoidal fuzzy numbers based on the relative preference relationAppl Math39586599","journal-title":"Appl Math"},{"key":"e_1_3_2_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(99)00062-7"}],"container-title":["Journal of Intelligent &amp; 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