Interval estimations of global weights in AHP by upper approximation

Authors:
Tomoe Entani;Hideo Tanaka
Affiliations:
Kochi University, 2-5-1 Akebono, Kochi 780-8520, Japan;Hiroshima International University, Gakuendai 555-36,Kurose, Hiroshima 724-0695, Japan
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

In analytic hierarchy process (AHP) structured hierarchically as several criteria and alternatives, the priority of an alternative is obtained by using the pairwise comparisons based on a decision maker's intuition. Thus, the given comparisons are uncertain and inconsistent with each other. We use the interval approach for obtaining interval evaluations which are suitable for handling uncertain data. Since the given comparisons are ratio measures and too large intervals are not useful information, the intervals should be normalized and their redundancy should be reduced. We introduce interval probability which fills the role of interval normalization instead of crisp normalization in the estimations at each hierarchy. Then, as a final decision, the interval global weights reflecting the decision maker's uncertain judgements as their widths without redundancy are obtained.