An approach to AHP decision in a dynamic context

Abstract

Abstract. AHP (analytic hierarchy process) is used to construct coherent aggregate results from preference data provided by decision makers. Pairwise comparison, used by AHP, shares a common weakness with other input formats used to represent user preferences, namely, that the input mode is static. In other words, users must provide all the preference data at the same time, and the criteria must be completely defined from the start. To overcome this weakness, we propose a framework that allows users to provide partial and/or incomplete preference data at multiple times. Since this is a complicated issue, we specifically focus on a particular aspect as a first attempt within this framework. For that reason, we re-examine a mechanism to achieve consistency in AHP, i.e. a linearization process, which provides consistency when adding a new element to the decision process or when withdrawing an obsolete criterion under the dynamic input mode assumption. An algorithm is developed to determine the new priority vector from the users' new input. Finally, we apply the new process to a problem of interest in the water field, specifically, the adoption of a suitable leak control policy in urban water supply.

A simple formula to find the closest consistent matrix to a reciprocal matrix

“…Given the great simplicity of the proposed formula, involving only sums, computational efficiency is guaranteed and integration in any AHP-based DSS is straightforward and of great interest. Finally, various applications of the Linearization Method (see, for example, [15,16]) can also benefit in a straightforward way from the obtained simplicity.…”

Consistent completion of incomplete judgments in decision making using AHP

“…In [5] we consider that AHP methodology can be thought as a dynamic model, following the idea that input in decision-making depends on whether actors indicate their preferences once or at several times. We presented mechanisms for adding and deleting criteria efficiently to preserve the work previously done on consistency with the criteria used so far.…”

“…This task is within a project for assessing the best leakage control alternative [14] that was specifically developed by the authors with Valencia's main water utility. Many of the matrices obtained in the course of this project have already been used by the authors in previous works [3,4,5,6,13]. The matrix in Table 1 was not considered in the main decision-making process as it was incomplete.…”

“…However, as a precondition, some actors may not be completely familiar with one or more of the elements about which they have to issue their judgment or opinion. The authors have addressed this issue in [5] for a specific scenario: the addition or deletion of a criterion. In leakage control, for example, only economic aspects have so far been considered.…”

“…In Section 4 we provide a full matrix termination mechanism for an incomplete comparison matrix produced by an actor. This mechanism uses an algebraic method (instead of optimization processes) to minimize a distance in a matrix set (see [5,Sec. 2.2] for a justification of this metric).…”