## 6 Results and Discussion
Average rank (criteria \(i=1,2,\ldots,m\); experts \(j=1,2,\ldots,n\)):  
\[\overline{R}=\frac{1}{2}n(m+1)=\frac{1}{2}14(10+1)=77,\]  
and sum of squared deviations (Table 4):  
\[S=\sum_{j=1}^{m}\left[\sum_{j=1}^{m}R_{ij}-\frac{1}{2}n(m+1)\right]^{2}=6842.\]  
Concordance coefficient (Formula (4)):  
\[W=\frac{12S}{n^{2}(m^{3}-m)}=\frac{12\cdot 6842}{14^{2}(10^{3}-10)}=0.423.\]  
The smallest value of the concordance coefficient \(W_{\min}\), when the significance level \(\alpha\) = 0.05 and the number of degrees of freedom \(\
u=m-1=10-1=9\):  
\[W_{\min}=\frac{\chi_{\
u,\alpha}^{2}}{n(m-1)}=\frac{\chi_{0.05,9}^{2}}{14(10-1 )}=\frac{16.919}{126}=0.134.\]  
[PERSON]'s criterion statistic:  
\[\chi^{2}=n(m-1)W=14(10-1)0.423=53.3\]  
or for the control:  
\[\chi^{2}=\frac{12S}{nm(m+1)}=\frac{12\cdot 6842}{14\cdot 10(10+1)}=53.3.\]  
The fact that the experts' opinions are aligned is shown by the new compatibility coefficient:  
\[k_{c}=\frac{W}{W_{\min}}=\frac{\chi^{2}}{\chi_{\alpha,\
u}^{2}}=\frac{0.423}{ 0.134}=\frac{53.3}{16.92}=3.15.\]  
Three times higher than the minimum concordance coefficient calculated by \(k_{c}\) from the criteria ranks allows us to reasonably assume that the opinions of the 14 expert groups are not contradictory in determining the normalized weights of the 10 criteria using the ARTIW-L, ARTIW-N, DPW, and AHP methods. Criteria weights determined by the ARTIW-L method (Formula (3)). The weight of the first criterion A is calculated:  
\[\omega_{A}=\frac{(m+1)-\overline{R}_{i}}{\sum_{i=1}^{m}\overline{R}_{i}}= \frac{(10+1)-7.286}{55}=0.0675.\]  
The calculated weights of other criterions and the priorities of these criterions are presented in Table 4.  
The criteria weights calculated by the ARTIW-N method (Formulas (9) and (10)) show that the average of the ranks of the most important criterion D is \(\overline{R}_{D}=2.643\), so its \(u_{D}=1\), and the other criteria \(u_{i}\) are less than 1. The normalized criteria weights \(\omega_{i}\) and their priorities are given in \[\overline{R}=\frac{1}{2}n(m+1)=\frac{1}{2}14(10+1)=77,\]0  
The first criterion A weight is \(\omega_{A}=\frac{0.3628}{5.5416}=0.0655\). The weights \(\omega_{i}\) of other criteria were calculated similarly. The criterions priorities calculated by the ARTIW-L and ARTIW-N methods coincide, but the criteria weights \(\omega_{i}\) differ. The percentage weights given to the experts' criteria (Table 5) were used to calculate the normalized weights \(\omega_{i}\) of these criteria using the DPW method according to Formula (11). The sum of percentage weights of the first criterion A is \(\sum_{j=1}^{n}P_{Ai}=86.3\), and the average of its percentage weights is \(\overline{P}_{A}=6.1643\). Therefore, the normalized weight of this criterion A is \(\omega_{A}=0.0616\). The weights \(\omega_{i}\) and priorities of other criterions (B, C, D, E, F, G, H, I and J) are calculated analogously. The criteria weights determined by the DPW method are similar to the weights calculated by the ARTIW-L and ARTIW-N methods. However, the difference between the weights of the most important D and the least important C or H criteria is greater as calculated per DPW method accuracy is much higher. The priorities of the criteria are identical, except for criteria C and H.  
The criteria's normalized weights \(\omega_{i}\) and compatibility ratios \(C.R.\) were calculated by the AHP method of the pairwise comparison matrices of the criteria filled out by each expert and presented in \[\overline{R}=\frac{1}{2}n(m+1)=\frac{1}{2}14(10+1)=77,\]1 All matrixes were concordant (\(C.R.<0.1\)) except for E7 expert (\(C.R.=0.105\)). Therefore, with a small margin of error, all matrixes were used to calculate the general opinion about the significance of the criteria for a group of 14 experts. The sums of the weights \(\sum_{j=1}^{n}\omega_{ij}\) of each \(i\)-th criterion were divided by the number of experts \(n=14\).