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Weak Consistency: A New Approach to Consistency in the Saaty’s Analytic Hierarchy Process
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 71-83 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 62C86
Keywords: decision making; consistency; Saaty’s AHP 
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Jandová, Věra; Talašová, Jana. Weak Consistency: A New Approach to Consistency in the Saaty’s Analytic Hierarchy Process. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 71-83. http://geodesic.mathdoc.fr/item/AUPO_2013_52_2_a6/

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