Increases dramatically as the number of decision alternatives increases. Having an acceptable level of inconsistency and are at risk for over-specification) The analysis reveals that, as expected, the risk of rank reversal (in matrices Over-specified hierarchies and the rank reversal phenomenon, via Monte Carlo The second focus of the thesis is to investigate any potential link between Inconsistency will generate smaller minimal priority weights. Moreover, we numerically show that the minimal priority weight is aĭecreasing function of the consistency ratio, indicating that higher levels of Matrix for that set and use its smallest priority weight as the minimal weight for theĮntire set. Within each set, we propose a representative For higher dimension pairwise comparison matrices, the concept ofĪ consistency ratio set is used to group potential pairwise comparison matrixes according to their consistency ratios. Matrix, the minimal possible priority weight is shown to be a unique function of theĬonsistency ratio. For the case of a 3x3 pairwise comparison The first focus of the thesis is to extend their methodology for the case ofĪn inconsistent pairwise comparison matrix. However, they assumed perfect consistency when determining the minimal possible If the priority weight associated with a specificĪlternative/criterion is within 10% of the corresponding minimal possible weight, theĪlternative/criterion should be considered for omission from the decision hierarchy. They suggested using the minimal priority weight to detect an Priority weight, the smallest priority weight for any alternative/criterion among nĪlternatives/criteria. (omitting relevant criteria/alternatives).Īull-Hyde and Duke (2006) introduced the concept of a minimal possible Table-1 shows the important evaluation scales of pair-wise comparison. Over-specification (including irrelevant criteria/alternatives) and underspecification the alternatives to obtain the matrix weight.
The initial step in applying AHP is toĪccurately decompose a decision problem into a decision hierarchy, avoiding both the Process is a multi-criteria decision making tool. Saaty in the early 1970’s, the Analytic Hierarchy Department: University of Delaware, Department of Food and Resource EconomicsĪbstract: Developed by Dr.