## 5 Criteria Significance Research Methods
### Analytic Hierarchy Process (AHP) Method  
The hierarchy analysis method is usually called analytic hierarchy process (AHP) method. It allows the criteria arranged at the beginning to be compared with each other in terms of importance, giving them a quantitative priority in relation to each other, expressed by the intensity (level) of the mutual importance of the two criteria. The essence of the method consists of the square matrix \(A\) of pairwise comparison. The expert compareswith each other all the criteria (factors, indicators) \(C_{i}\) and \(C_{j}\) (\(i,j=1,\,2,\,\ldots,\,m\)) that make up the object, where m is the compared criteria (factors increasing the relative amount of asphalt pavement recycling (\(K_{Rec}\) in the country) number. The Saaty scale of five levels of importance (1-3-5-7-9) is used to compare the criteria. Intermediate even estimates (2-4-6-8) can also be used. The AHP method is convenient because it is easier for the expert to compare the factors that increase the relative amount of asphalt pavement recycling in the \(K_{Rec}\) country, two at a time, instead of all at once. Such a comparison of criteria is simple and reliable only for an expert who is well versed in the AHP method, and especially in the principles of filling in the pairwise comparison matrix. A matrix indicates how much one of its elements is more important than another element. The method allows the qualitative (linguistic, verbal) assessment of factors (criteria) to be presented in a quantitative (numerical) assessment. The result of the pairwise comparison of the criteria is the square matrix \(A=\left\|a_{ij}\right\|_{m\times m}\) (\(i,j=1,\,2,\,\ldots,\,m\)). Comparing the importance of factors \(C_{i}\) and \(C_{j}\), which increase the relative amount of asphalt pavement recycling \(K_{Rec}\) in country, it is marked by estimates \(\omega_{1}\), \(\omega_{2}\), \(\ldots\), \(\omega_{m}\) the ratio:  
\[a_{ij}=\frac{\omega_{i}}{\omega_{j}}(i,j\,\,=\,\,1,\,2,\,\ldots,\,\,m) \tag{12}\]  
shows how many times the \(i\)-th factor (criterion) \(C_{i}\) is more important than the \(j\)-th factor \(C_{j}\), \(a_{ij}=1/a_{ji}\). The elements of matrix \(A\) (whole and fractional numbers on a nine-point scale) are filled in according to the following requirements. The elements of matrix \(A\)\(a_{ij}=1\), when the significance of both compared criteria in relation to the research object (\(K_{Rec}\)) is the same. In this case, all elements of the main diagonal \(a_{ij}=1\) (\(i=1,\,2,\,\ldots,\,m\)) since each criterion is compared with itself. The elements of the matrix \(A\)\(a_{ij}=3\), when the criterion \(C_{i}\) is slightly more important than the criterion \(C_{j}\). The elements of matrix \(A\)\(a_{ij}=5\) when the criterion \(C_{i}\) is much more important than the criterion \(C_{j}\). The elements of the matrix \(A\)\(a_{ij}=7\), when the criterion \(C_{i}\) is very much (significantly) more important than the criterion \(C_{j}\). The elements of the matrix \(A\)\(a_{ij}=9\), when the criterion \(C_{i}\) is incomparably (absolutely) more important than the criterion \(C_{j}\) (Table 2). The elements \(a_{ij}\) of the matrix \(A\) can be considered as the ratio of the values of the criteria \(C_{i}\) and \(C_{j}\) after the normalization of these values--as the ratio of the weights of the criteria. The square matrix of the pairwise comparison of the criteria assessed by one expert looks like this (\(i\)--rows, \(j\)--columns):  
\[A= \begin{bmatrix}a_{11}&a_{12}&\ldots&a_{1j}&\ldots&a_{1m}\\ a_{21}&a_{22}&\ldots&a_{2j}&\ldots&a_{2m}\\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\ a_{i1}&a_{i2}&\ldots&a_{ij}&\ldots&a_{im}\\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\ a_{m1}&a_{m2}&\ldots&a_{mj}&\ldots&a_{mm}\end{bmatrix}