{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T18:10:11Z","timestamp":1754158211070,"version":"3.41.2"},"reference-count":16,"publisher":"Emerald","issue":"2","license":[{"start":{"date-parts":[[2016,8,1]],"date-time":"2016-08-01T00:00:00Z","timestamp":1470009600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016,8,1]]},"abstract":"\n Purpose<\/jats:title>\n \u2013 Until now, many different varieties of grey relational grade methods had been proposed, and there are also many relevant publications. However, in one article published in 2007, which applied the previous grey relational grade to environmental protection fields and some results had been found. After studied it carefully, the author found that the grey relational grade in the paper was not the previous grey relational grade. According to the mathematics logic, it must first prove the proposed grey relational grade satisfies the four axioms in grey relational analysis, and then the author can say that the achieved results are reasonable and correct. The paper aims to discuss these issues. <\/jats:p>\n <\/jats:sec>\n \n Design\/methodology\/approach<\/jats:title>\n \u2013 The paper lists the rational and regular grey relational grade that had been published in the past, and used the four axioms in grey system theory to prove the Pai\u2019s grey relational grade that satisfy the four axioms steps by steps. <\/jats:p>\n <\/jats:sec>\n \n Findings<\/jats:title>\n \u2013 Through the detail proof of the proposed grey relational grade in Pai\u2019s paper, it indeed satisfies the four axioms in grey relational grade. <\/jats:p>\n <\/jats:sec>\n \n Research limitations\/implications<\/jats:title>\n \u2013 The paper had enhanced the correctness and reasonableness of that paper, and let the grey relational grade, which appear in Pai\u2019s paper is legitimate and correct grey relational grade in grey system theory. <\/jats:p>\n <\/jats:sec>\n \n Originality\/value<\/jats:title>\n \u2013 The paper had identified that Pai\u2019s grey relational grade is a rational and regular grey relational grade in grey system theory, and it proves that the results in Pai\u2019s paper are correct and reasonable.<\/jats:p>\n <\/jats:sec>","DOI":"10.1108\/gs-02-2016-0007","type":"journal-article","created":{"date-parts":[[2016,7,26]],"date-time":"2016-07-26T05:55:36Z","timestamp":1469512536000},"page":"180-186","source":"Crossref","is-referenced-by-count":7,"title":["The proof of a new modified grey relational grade"],"prefix":"10.1108","volume":"6","author":[{"given":"Kunli","family":"Wen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"140","reference":[{"key":"key2020121320164245400_b1","unstructured":"Chen, M.L.\n , \n You, M.L.\n , \n Lin, C.H.\n and \n Su, P.Y.\n (2014), \u201cThe rational of cardinal grey relational grade\u201d, \n Journal of Grey System\n , Vol. 17 No. 4, pp. 193-198."},{"key":"key2020121320164245400_b2","unstructured":"Dang, Y.G.\n (1995), \u201cStudy on grey slope incidence degree\u201d, \n System Science and Comprehensive Studies in Agricultural\n , No. 10, pp. 331-337."},{"key":"key2020121320164245400_b3","unstructured":"Deng, J.L.\n (1989), \u201cThe introduction of grey system theory\u201d, \n The Journal of Grey System\n , Vol. 1 No. 1, pp. 1-24."},{"key":"key2020121320164245400_b4","unstructured":"Hsia, K.H.\n and \n Wu, J.H.\n (1998), \u201cA study on the data preprocessing in grey relation analysis\u201d, \n Journal of Grey System\n , Vol. 1 No. 1, pp. 47-53."},{"key":"key2020121320164245400_b5","unstructured":"Liu, S.F.\n , \n Xie, N.M.\n and \n Forrest, J.\n (2008), \u201cA kind of new models for grey incidence analysis\u201d, \n Science Paper Online\n , Vol. 1 No. 12, pp. 1328-1336."},{"key":"key2020121320164245400_b6","doi-asserted-by":"crossref","unstructured":"Pai, T.Y.\n , \n Hanaki, K.S.\n , \n Hoa, H.H.\n and \n Hsieh, C.M.\n (2007), \u201cUsing grey system theory to evaluate transportation effects on air quality trends in Japan\u201d, \n Transportation Research Part D: Transport and Environment\n , Vol. 12 No. 3, pp. 158-166.","DOI":"10.1016\/j.trd.2007.01.007"},{"key":"key2020121320164245400_b7","unstructured":"Tang, W.X.\n (1989), \u201cThe concept and computation method of T\u2019s correction degree\u201d, \n Application of Statistics and Management\n , Vol. 14 No. 1, pp. 33-37."},{"key":"key2020121320164245400_b8","unstructured":"Wang, Q.Y.\n (1989), \u201cThe grey relational analysis of B-mode\u201d, \n Journal of Huazhong University of Science and Technology\n , Vol. 17 No. 6, pp. 77-82."},{"key":"key2020121320164245400_b9","unstructured":"Wen, K.L.\n (1999), \u201cThe cardinal form of grey relational grade\u201d, \n Journal of Grey System\n , Vol. 2 No. 2, pp. 117-133."},{"key":"key2020121320164245400_b10","unstructured":"Wen, K.L.\n (2004), \n Grey Systems Modeling and Prediction\n , Yang\u2019s Scientific Research Institute."},{"key":"key2020121320164245400_b11","unstructured":"Wen, K.L.\n (2013), \n Grey System Theory\n , 2nd ed., Wunan Publisher, Taipei."},{"key":"key2020121320164245400_b12","unstructured":"Wong, C.C.\n and \n Lai, H.R.\n (2000), \u201cA new grey relational measurement\u201d, \n The Journal of Grey Systems\n , Vol. 12 No. 4, pp. 341-346."},{"key":"key2020121320164245400_b13","unstructured":"Wu, J.H.\n and \n Chen, C.B.\n (1999), \u201cAn alternative form for grey relational grades\u201d, \n The Journal of Grey System\n , Vol. 11 No. 1, pp. 7-12."},{"key":"key2020121320164245400_b14","unstructured":"Yamaguchi, D.S.\n , \n Li, G.D.\n and \n Nagai, M.M.\n (2005), \u201cNew grey relational analysis for finding the invariable structure and its applications\u201d, \n Journal of Grey System\n , Vol. 8 No. 2, pp. 167-178."},{"key":"key2020121320164245400_b15","unstructured":"Yeh, M.F.\n and \n Lu, H.C.\n (2016), \u201cA bipolar type of cardinal grey relational grade\u201d, \n Journal of Grey System\n , Vol. 19 No. 1, pp. 1-6."},{"key":"key2020121320164245400_b16","unstructured":"You, M.L.\n , \n Chen, W.T.\n and \n Wen, K.L.\n (2014), \u201cThe imperfection of ordinal grey relational grade in grey system theory\u201d, \n Journal of Grey System\n , Vol. 17 No. 2, pp. 67-76."}],"container-title":["Grey Systems: Theory and 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