Title: A method for improving cosine consistency index of pairwise comparison matrix in analytic hierarchy process

Authors: L.N.P. Kumar Rallabandi; Ravindranath Vandrangi

Addresses: Department of Mathematics, Vishnu Institute of Technology (A), Bhimavaram, A.P., 534202, India ' Department of Mathematics, JNT University Kakinada, Kakinada, A.P., 530003, India

Abstract: In analytic hierarchy process (AHP), pairwise comparison matrix (PCM) is used to rank the alternatives in the decision-making problem. The priority vector, derived from the PCM, is accepted only when the PCM is consistent. However, in many practical situations the PCM obtained by the judgments of expert may be inconsistent. Several indices have been proposed to measure the consistency level of PCM over the years and one among them is cosine consistency index (CCI). In this paper, an algorithm is proposed to improve the consistency of PCM in terms of CCI. For examining the consistency of the given PCM, the new threshold values for CCI are proposed. Correlation and regression analysis is used to derive the relation between CCI and consistency ratio (CR) from which the threshold values of CCI for PCMs of order 3 to 15 are determined. The derived regression models have been validated by using statistical techniques.

Keywords: cosine consistency index; CCI; pairwise comparison matrix; PCM; consistency ratio; analytic hierarchy process; AHP.

DOI: 10.1504/IJMOR.2022.127052

International Journal of Mathematics in Operational Research, 2022 Vol.23 No.2, pp.259 - 283

Received: 02 Mar 2021
Accepted: 07 Jul 2021
Published online: 21 Nov 2022 *

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