Title: A binomial simulation approach to more consistent AHP matrices

Authors: Phillip W. Witt; Mohsen Hamidi

Addresses: Department of Strategic Management and Operations, Woodbury School of Business, Utah Valley University, Orem, UT, 84058, USA ' Department of Strategic Management and Operations, Woodbury School of Business, Utah Valley University, Orem, UT, 84058, USA

Abstract: Different methods have been proposed for simulating analytical hierarchy process (AHP) matrices. In this paper, we develop a new method assuming responses for AHP matrices follow binomial distributions. In this paper, we exhibit the method with a small data sample which we use to estimate the binomial parameters by transformation, and then backwards solving the logit Newton-Raphson updating algorithm. A parametric bootstrap sample is then used to compare the simulated results against the actual results from the data. In addition to the new simulation method we discover some interesting findings regarding AHP matrix consistency.

Keywords: analytic hierarchy process; AHP; simulation; decision-making; group decision-making; decision science; managerial decision-making; consistency; Newton-Raphson; binomial.

DOI: 10.1504/IJIDS.2025.150098

International Journal of Information and Decision Sciences, 2025 Vol.17 No.4, pp.343 - 356

Received: 03 Aug 2022
Accepted: 04 Aug 2023
Published online: 01 Dec 2025 *

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