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**Weak consistency: a new approach to consistency in the Saaty’s analytic hierarchy process.**
*(English)*
Zbl 1292.62021

Summary: In the decision making methods based on the pairwise comparison there is very important to enter the preferences of compared elements in the rational way. Only in this case we are able to obtain the reasonable solution. In the Analytic Hierarchy Process (AHP) there is set a strict consistency condition in order to keep the rationality of preference intensities between compared elements. But this requirement for the Saaty’s matrix is not achievable in the real situations because of the Saaty’s scale which is used in this method. That is why instead of the consistency condition we suggest a weak consistency condition which is very natural and more suitable for the linguistic descriptions of the Saaty’s scale and as a result of it, it is easier to reach this requirement in the real situations. In addition, if we order compared elements from the most preferred to the least preferred, it is very easy to check if the weak consistency is satisfied. Big advantage of our approach to the consistency is that its satisfaction can be easily approved. It is also possible to control the weak consistency of the Saaty’s matrix during the filling of the intensities of preferences. We also show on the example that there can be situations in which the weak consistency condition is more suitable for checking the rationality of the preferences than the Saaty’s consistency ratio.

### MSC:

62C86 | Statistical decision theory and fuzziness |

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\textit{V. Jandová} and \textit{J. Talašová}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 52, No. 2, 71--83 (2013; Zbl 1292.62021)

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