*4.2. Practical Application and Analysis of the Implementation of the Second Algorithm for Checking the Stability*

Using the second algorithm for checking the stability, the elements of the pairwise comparison matrix are changed by one. The stability of the method is also set by the different numbers of iterations: 100, 10,000, and 100,000. The value of the relative errors *δ ξ* of the values of the criteria weights is fixed. In each case, ten attempts are made to fix the range of the relative errors. In the first case, the matrix data with a good consistency index are used (Table 1). Table 9 shows the results of ten attempts to check the stability of the method, and the largest relative errors *δ ξ* , with the number of iterations equal to 100, using the first matrix data (Table 1). The results show small *δ <sup>ξ</sup>* values of the largest relative errors of the weights of the criteria. Comparing the results for the relative errors of the weights of the criteria (Table 10) with the results of the first algorithm (a deviation of 10%) (Table 3), the results have increased on average by 23%.


**Table 9.** The largest relative errors of the criteria weights *δ ξ* , when checking the stability by the second algorithm, 100 iterations, 10 repetitions, 1st matrix.

**Table 10.** The interval of the largest relative errors of the criteria weights *δ ξ* , when checking the stability by the second algorithm, 10 repetitions, 1st matrix.


Checking the consistency of the first matrix, the results of checking the second algorithm for the largest relative errors *δ ξ* (Table 10) are less than with a 10% data deviation, but more than with a 5% deviation. With the number of iterations equal to 100,000, the intervals of the criteria are practically narrowed to one value.

When checking the consistency of the matrices using the first matrix, all the other generated matrices are consistent, in contrast to the second matrix, in which 55–70% of the matrices are inconsistent and discarded (Table 11).

**Table 11.** The percentage of consistent matrices when checking the stability by the second algorithm using the data of the first and second matrices.


The largest relative error *δ <sup>ξ</sup>* of the results for the second matrix is small (Table 12). The results turn out to be better than when using the first matrix and the same algorithm. This can be explained by the smaller number of consistent matrices used (30–45%).

**Table 12.** The interval of the largest relative errors of the criteria weights *δ ξ* , when checking the stability by the second algorithm, 10 repetitions, 2nd matrix.


In both verification cases, the results show the stability of the method: *δ* = 0.5121 (using the first matrix) and *δ* = 0.7739 (using the second matrix).
