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A pairwise comparison matrix in the Analytic Hierarchy Process (AHP), which was proposed by Saaty in 1970s, consists of elements expressed on a numerical scale. The purpose of this paper is to propose a consistency test for ordinality of items in the pairwise comparison matrix. The original of this test is in a sensory test. In a sensory test we use a pick-the-winner ordinal scale to obtain the table of preferences for objects. In 1940 Kendall and Babington Smith proposed a consistency test for the preference table, using the number of circular triads in it. In this paper we show how to apply their test to a pairwise comparison matrix in the binary AHP and to one without a tie for up to nine items in the AHP. This is to test, using a pairwise comparison matrix, whether or not we can accept that items which are factors or alternatives are sufficiently ranked linearly before calculating weights of these items.

journal of the operations research society of japan

THE NUMBER OF CIRCULAR TRIADS IN A PAIRWISE COMPARISON MATRIX AND A CONSISTENCY TEST IN THE AHP(&lt;Special Issue&gt;Operations Research for Performance Evaluation)