Uncertainty index based interval assignment by Interval AHP

Uncertainty index based interval assignment by Interval AHP

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Article ID: iaor20122124
Volume: 219
Issue: 2
Start Page Number: 379
End Page Number: 385
Publication Date: Jun 2012
Journal: European Journal of Operational Research
Authors: ,
Keywords: statistics: inference, matrices, analytic hierarchy process
Abstract:

In a multi‐attribute decision making problem, indigenous values are assigned to attributes based on a decision maker’s subjective judgments. The given judgments are often uncertain, because of the uncertainty of situations and intuitiveness of human judgments. In order to reflect the uncertainty in the assigned values, they are denoted as intervals whose widths represent the possibilities of attributes. Since it is difficult for a decision maker to assign values directly to attributes in case of more than two attributes, he/she gives a pairwise comparison matrix by comparing two attributes at one occasion. The given matrix contains two kinds of uncertainty, one is inconsistency among comparisons and the other is incompleteness of comparisons. This paper proposes the models to obtain intervals of attributes from the given uncertain pairwise comparison matrix. At first, the uncertainty indexes of a set of intervals are defined from the viewpoints of entropy in probability, sum or maximum of widths, or ignorance. Then, considering that too uncertain information is not useful, the intervals of attributes are obtained by minimizing their uncertainty indexes.

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