Interval Evaluations in the Analytic Hierarchy Process By Possibility Analysis |
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Authors: | Kazutomi Sugihara,& Hideo Tanaka |
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Affiliation: | Department of Applied Physics, Graduate School of Engineering, Osaka University, Japan;, Graduate School of Management and Information Science, Toyohashi Sozo College, Japan |
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Abstract: | Since a pairwise comparison matrix in the Analytic Hierarchy Process (AHP) is based on human intuition, the given matrix will always include inconsistent elements violating the transitivity property. We propose the Interval AHP by which interval weights can be obtained. The widths of the estimated interval weights represent inconsistency in judging data. Since interval weights can be obtained from inconsistent data, the proposed Interval AHP is more appropriate to human judgment. Assuming crisp values in a pairwise comparison matrix, the interval comparisons including the given crisp comparisons can be obtained by applying the Linear Programming (LP) approach. Using an interval preference relation, the Interval AHP for crisp data can be extended to an approach for interval data allowing to express the uncertainty of human judgment in pairwise comparisons. |
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Keywords: | AHP interval evaluations possibility analysis |
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