**3. Stability Check for the AHP and FAHP Methods**

The AHP and FAHP methods are applied in Multicriteria Decision-Making (MCDM) evaluations in order to determine the criteria weights. The AHP method is applied in the deterministic case when the significance (weight) of each of the criteria is determined with one number. In this case, each expert determines the criterion significance in the matrix of pairwise comparisons of the criteria with one number (taken from the Saaty scale: 1-3-5-7-9). The FAHP method is used in conditions of data uncertainty when interval fuzzy evaluations are used for the calculations. In this case, evaluations of the pairwise comparison of the criteria (that is, the values of the FAHP method matrix) are also represented by interval fuzzy numbers.

The criteria weights can be used in the MCDM model methods if the weight evaluation methods, that is, the AHP and FAHP methods, are stable (resistant) in relation to natural random variations of the evaluations. Considering that the value *M* of a triangular fuzzy number is matched with the most probabilistic evaluation of the AHP method, it would be of interest to perform a parallel investigation of stability for the AHP and FAHP methods. The references suggest more than 25 scales that can be used in order to form the triangular values of the triangular fuzzy numbers. The frequently applied symmetric and asymmetric scales of triangular fuzzy numbers are used in this paper.

The stability of the AHP method can be understood in two ways: the stability of just the method, which depends upon the essence of the method or its mathematical basis, and the stability of the results, that is, the values of the criteria weights depending upon the evaluations provided by the experts that vary due to the uncertainty inherent to their thinking processes.

Both stability options are studied in this paper.
