Scale transitivity in the AHP

Ping Ji · Renyan Jiang

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Multi-Criteria Decision Making Game Theory and Voting Systems Strategic Planning and Analysis

Abstract

Transitivity is important in multicriteria decision-making. The analytic hierarchy process (AHP), as one of the widely used decision analysis tools, is criticized since it suffers from scale intransitivity. This paper first reviews and compares different scales from different aspects, then discusses the transitivity of AHP scales and derives a scale based on the transitivity, so it is naturally transitive. Besides, two approaches are provided to determine the scale parameter for the derived transitive scale. In order to deal with the transitivity problem, the AHP provides a consistency index for testing pairwise comparison consistency. So, finally, this paper proposes a consistency measure to reflect the judgmental inconsistency.

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References

1985The Analytic Hierarchy Process 1977A scaling method for priorities in hierarchical structures 2001The Analytic Hierarchy Process—An Exposition 1990An overview of the analytic hierarchy process and its applications 1987The Theory of Ratio Scale Estimation: Saaty's Analytic Hierarchy Process 1994Highlights and critical points in the theory and application of the Analytic Hierarchy Process 1997On the measurement of preferences in the analytic hierarchy process 1997Deriving weights from pairwise comparison matrices

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