The proof of a new modified grey relational grade

Purpose - 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. Design/methodology/approach - 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's grey relational grade that satisfy the four axioms steps by steps. Findings - Through the detail proof of the proposed grey relational grade in Pai's paper, it indeed satisfies the four axioms in grey relational grade. Research limitations/implications - The paper had enhanced the correctness and reasonableness of that paper, and let the grey relational grade, which appear in Pai's paper is legitimate and correct grey relational grade in grey system theory. Originality/value - The paper had identified that Pai's grey relational grade is a rational and regular grey relational grade in grey system theory, and it proves that the results in Pai's paper are correct and reasonable.