{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:38:02Z","timestamp":1777703882035,"version":"3.51.4"},"reference-count":30,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2019,6,14]],"date-time":"2019-06-14T00:00:00Z","timestamp":1560470400000},"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":[[2019,10,25]]},"abstract":"<jats:p>\n                    In this paper, the\n                    <jats:italic>\u03b1<\/jats:italic>\n                    -satisfactory goal programming (GP) method is proposed for multi-objective optimization (MOO) with priorities and fuzzy parameters. Fuzzy parameters are treated as fuzzy numbers, and all objectives are modeled into fuzzy goals over\n                    <jats:italic>\u03b1<\/jats:italic>\n                    -level sets. The order of\n                    <jats:italic>\u03b1<\/jats:italic>\n                    -satisfactory degrees is applied to preemptive priority requirement, where the\u00a0objectives with higher priority can achieve the higher\n                    <jats:italic>\u03b1<\/jats:italic>\n                    -satisfactory degree. In order to guarantee the feasibility and seek the\u00a0preferred solution, a priority variable is introduced to relax the strict order. For three fuzzy relations, GP is combined with the relaxed order constraint to formulate the different\n                    <jats:italic>\u03b1<\/jats:italic>\n                    -satisfactory optimization models. By regulating optimization parameters\n                    <jats:italic>\u03bb<\/jats:italic>\n                    and\n                    <jats:italic>\u03b1<\/jats:italic>\n                    , the most satisfactory solution over fuzzy parameters can be obtained, and the balance between optimization and priority can be realized. The reformulated\n                    <jats:italic>\u03b1<\/jats:italic>\n                    -GP models are proved to be feasible, and their solutions are guaranteed to be M-\n                    <jats:italic>\u03b1<\/jats:italic>\n                    -Pareto optimal by the test model. In order to decrease optimization burden, the algorithm to compute the\n                    <jats:italic>\u03b1<\/jats:italic>\n                    -maximum regulating parameter is proposed, by which the bound of\n                    <jats:italic>\u03bb<\/jats:italic>\n                    can be determined. The effectiveness of the proposed method is well demonstrated by numerical examples.\n                  <\/jats:p>","DOI":"10.3233\/jifs-18904","type":"journal-article","created":{"date-parts":[[2019,6,18]],"date-time":"2019-06-18T12:23:15Z","timestamp":1560860595000},"page":"5167-5178","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["<i>\u03b1<\/i>\n                    -Satisfactory goal programming method for multi-objective optimization with priorities and fuzzy parameters"],"prefix":"10.1177","volume":"37","author":[{"given":"Chaofang","family":"Hu","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin, China"},{"name":"Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin, China"},{"name":"Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Tianjin University, Tianjin, China"},{"name":"Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yimin","family":"Zhou","sequence":"additional","affiliation":[{"name":"Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baocang","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Electric and Information Engineering, Xian Jiaotong University, Xian, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,6,14]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"crossref","unstructured":"LaiY.J. and HwangC.L. 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