Implementation and application of gray fuzzy decision in English teaching quality

As a system distinguishing decision, the gray decision can solve most of the issues related to the gray fuzzy multi-criteria decision in real life. This paper establishes a gray fuzzy decision model based the English teaching quality, in order to evaluate the English teaching quality. The model defines the fuzzy set according to the index attributes, and gives the membership for the gray fuzzy relations between indices, and then obtains the weight results of each index based on the calculation of the gray fuzzy. Finally, this paper verifies the availability of the model through the actual teaching examples.


INTRODUCTION
English teaching quality is mainly manifested in the objective, systematic, normative, and efficiency and effectiveness principle of English teaching quality.A better teaching quality comes from joint action of each component.Each link of teaching shall be organized rationally, in order to form a good teaching quality assurance system.In the gray fuzzy decision model, the weight definition of AHP mainly includes: establishment of the hierarchical structure, construction of the judgment matrix and calculation of the relative weight, as well as calculation of the synthetic right of the attribute target.The weight definition can be used to obtain the evaluation results of better English teaching quality under a number of factors of the students, teachers, schools and so on.

ESTABLISHMENT OF GRAY FUZZY DECISION MODEL
Supposing that the target has n attributes (u 1 ,u 2 ,u 3 ,…,u n ), under the criterion C, two different attributes of u i and u j are compared.The importance degree of u i and u j are denoted by u ij and u ji under the criterion C. Where, u ij and u ji satisfy: However, the comparison of u i itself is meaningless.Setting that u ii =0 (1≤i≤n).
For the definition of the comparison with u ij and u ji : if u ij > u ji , then u i is more important than u j .
Consistency analysis: The judgment matrix of the attributes has a necessary and sufficient condition of consistency, for any i T is defined as the relative weight.The comparison matrix can be expressed as: Target layer: analysis of English teaching quality Criterion layer: c 1 is the objective principle; c 2 is the systematic principle; c 3 is the normative principle; c 4 is the principle of efficiency and effectiveness.
Result layer: A 1 is the students themselves; A 2 is the teaching materials and instructional design; A 3 is the teacher factor.
The hierarchical analysis system of the criterion layer is shown in Table 1.

Construction of the judgment matrix at each layer
The proportion of each criterion target at the criterion layer is different.Through the research of the criterion layer by the researchers, and according to the numbers from 1 to 9 and their reciprocal values, the proportion of each criterion target can be determined.This paper carries out the weight analysis based on the scale table of 1 to 9 shown in Table 2. First, the judgment matrix is solved.Based on the above principle, referring to the scale setting from 1 to 9, according to the experience of the experts and the author, and referring to a lot of literatures, the pairwise comparison matrices can be obtained, as shown in the following matrix.
Where, the comparison matrix A is the comparison matrix between the target layer and the criterion layer.The comparison matrix c 1 -c 4 is the comparison matrix between the criterion layer and scheme layer.In the criterion layer, there are comparison matrices of the objective principle, systematic principle, normative principle, and efficiency and effectiveness principle.

O
Where: λ max is the maximum eigenvalue; n is the order of the comparison matrix; the smaller the value of CI is, the closer to consistency the judgment matrix is.The greater the value of CI is, the lower the known degree is.

Total level sorting and consistency test
Through normalization of the column vector of the matrix A, 1 1/ 3 3 3 0.2514 1.012 3 1 5 5 0.555 2.275 1/ 3 1/ 5 1 1 0.0965 0.387 1/ 3 1/ 5 1 1 0.0965 0.387 In the process of solving the matrix A, similarly, the comparison matrices of the objective principle, sys-tematic principle, normative principle, and efficiency and effectiveness principle of English teaching quality are as follows: Thus, the eigenvalues and eigenvectors of the objective principle, systematic principle, normative principle, and efficiency and effectiveness principle of English teaching quality are as follows: (1) ( It corresponds to the index in each result layer.The hierarchical structure is established, as shown in Figure 1.

Figure 1 .
Figure 1.Second hierarchical structural diagram Comparison matrix of efficiency and effectiveness principle of English teaching quality:

Table 1 .
Hierarchical analysis system of the criterion layer

Table 2 .
Scale table of 1 to 9