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Until now, many different varieties of grey relational grade methods had been proposed, and there are also many relevant publications, which include ordinal grey relational grade and cardinal grey relational grade. However, the most original and important formula is Deng’s grey relational grade. After careful study it was found that although it is an ordinal form of grey relational grade, a rational mathematics model can be used to transfer it from ordinal into cardinal. It not only can enhance the essential of Deng’s grey relational grade, but also can let Deng’s grey relational grade be used more widely. The paper aims to discuss these issue.

The paper uses fuzzy set theory to get the rational value of distinguish coefficient in Deng’s grey relational grade, then uses grey entropy method to decide the rational weighting for the analysis sequences in Deng’s grey relational grade.

Through the mathematics derivation, it indeed can transfer the Deng’s grey relational grade from ordinal form into cardinal form.

The paper has deeply enhanced the essential of Deng’s grey relational grade, and made Deng’s grey relational grade more available and more usable in grey system theory.

The paper has transferred the Deng’s grey relational grade from ordinal into cardinal, it can let Deng’s grey relational grade be used in a wider area.

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.

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.

Through the detail proof of the proposed grey relational grade in Pai’s paper, it indeed satisfies the four axioms in grey relational grade.

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.

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.

Numerous smog events have occurred in recent years in China. Their hazards in mining and industrial cities are more serious than clear days. The samples were collected in the mining and industrial city of Handan. During the smog episode, PM₁₀ and PM_2.5 concentrations reach up to 980 μg/m³ and 660 μg/m³, respectively. Under SEM (scanning electron microscope) analysis, the particles consist of soot, fly ash and minerals, which could be from coal mines, power plants, steel mills and auto exhausts. Compared with the samples collected on a clear day, the increased PM₁₀ particles are mainly composed of organic matter, especially aromatic compounds. The Pb content in PM₁₀ of the smog day reaches 507.4 ng/m³ and could be caused by vehicle emissions.