Consistent completion of incomplete judgments in decision making using AHP

Decision making (DM) processes are becoming increasingly complex. The reasons are manifold. DM usually involves many aspects; some are purely technical, while others are subjective and derived from social, political, and environmental factors, among others. As a result, they involve items that are not easily comparable under the same units of measurement. Problems are made even more complex by the fact that current governance processes tend to involve all the stakeholders in the DM process. In this paper we consider the AHP methodology (analytic hierarchy process), which is used to build consistent aggregate results from data provided by decision makers. As some of the actors involved may not be completely familiar with all the criteria under consideration, it is common that the body of opinion, expressed in terms of pairwise comparison, is incomplete. To overcome this weakness, we propose a framework that enables users to provide data on their preferences in a partial and/or incomplete way and at different times. This article is an advance towards a dynamic model of AHP. The authors have addressed the problem of adding a new criterion or deleting obsolete criteria. Here, we address the consistent completion of a reciprocal matrix as a mechanism to obtain a consistent body of opinion issued in an incomplete manner by a specific actor. This feature is incorporated into a process of linearization previously introduced by the authors, which is concisely presented. Finally, we provide an application for leakage control in a water supply company. The adoption of suitable control leakage policies in water supply is a problem of enormous interest in the water industry, particularly in urban hydraulics.
This work has been funded as part of project IDAWAS, DPI2009-11591 by the Direccion General de Investigacion del Ministerio de Ciencia e Innovacion (Spain); with supplementary support from ACOMP/2011/188 from the Conselleria d'Educacio of the Generalitat Valenciana. The first author also received support from Spanish project PAID-06-12. The use of English in this paper was revised by John Rawlins.