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This notion is applied to cascade the grey objective function to a bi\u2010objective problem based on the objective function of the original problem. The same approach is taken to transform grey constraints to a set of corresponding linear constraints. Finally, the obtained multi\u2010objective model can be solved by any existing methods in the literature.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Findings<\/jats:title><jats:p>One of the shortcomings of previous approaches to solve grey linear programming problems was that they required the grey coefficients of objective function to be both side negative or positive. The approach proposed here does not have such a requirement and guarantees the feasibility of solutions.<\/jats:p><\/jats:sec><jats:sec><jats:title content-type=\"abstract-heading\">Originality\/value<\/jats:title><jats:p>A different approach is developed in the paper that can be used to solve grey linear programming problems in general form. The method relaxes the limitation of existing approaches.<\/jats:p><\/jats:sec>","DOI":"10.1108\/20439371211260225","type":"journal-article","created":{"date-parts":[[2014,11,13]],"date-time":"2014-11-13T12:10:36Z","timestamp":1415880636000},"page":"259-271","source":"Crossref","is-referenced-by-count":28,"title":["A multi\u2010objective programming approach to solve grey linear programming"],"prefix":"10.1108","volume":"2","author":[{"given":"Seyed","family":"Hossein Razavi Hajiagha","sequence":"first","affiliation":[]},{"given":"Hadi","family":"Akrami","sequence":"additional","affiliation":[]},{"given":"Shide","family":"Sadat Hashemi","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"key":"key2022031220072794500_b1","doi-asserted-by":"crossref","unstructured":"Bazaraa, M.S., Jarvis, J.J. and Sherali, H.D. 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(1959), \u201cChance constrained programming\u201d, Management Sciences, Vol. 6 No. 1, pp. 73\u20109.","DOI":"10.1287\/mnsc.6.1.73"},{"key":"key2022031220072794500_b5","doi-asserted-by":"crossref","unstructured":"Chen, Z., Chen, Q., Chen, W. and Wang, Y. (2004), \u201cGrey linear programming\u201d, Kybernetes, Vol. 33 No. 2, pp. 238\u201046.","DOI":"10.1108\/03684920410514166"},{"key":"key2022031220072794500_b6","unstructured":"Dantzig, G.B. (1948), \u201cProgramming in a linear structure\u201d, Comptroller, United States Air Force, Washington, DC."},{"key":"key2022031220072794500_b7","doi-asserted-by":"crossref","unstructured":"Dantzig, G.B. (1949), \u201cProgramming of interdependent activities II, mathematical model\u201d, Econometrica, Vol. 17 Nos 3\/4, pp. 200\u201011.","DOI":"10.2307\/1905523"},{"key":"key2022031220072794500_b8","doi-asserted-by":"crossref","unstructured":"Deng, J.L. (1982), \u201cControl problems of grey system\u201d, Systems and Control Letters, Vol. 1 No. 5, pp. 288\u201094.","DOI":"10.1016\/S0167-6911(82)80025-X"},{"key":"key2022031220072794500_b9","unstructured":"Deng, J.L. (1989), \u201cIntroduction to grey system theory\u201d, The Journal of Grey Theory, Vol. 1 No. 1, pp. 1\u201024."},{"key":"key2022031220072794500_b10","doi-asserted-by":"crossref","unstructured":"Guua, S.M. and Wu, Y.K. (1999), \u201cTwo\u2010phase approach for solving the fuzzy linear programming problems\u201d, Fuzzy Sets and Systems, Vol. 107 No. 2, pp. 191\u20105.","DOI":"10.1016\/S0165-0114(97)00304-7"},{"key":"key2022031220072794500_b11","doi-asserted-by":"crossref","unstructured":"Huang, G.H. 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