An approach to AHP decision in a dynamic context

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. © 2012 Elsevier B.V. All rights reserved.This work has been performed under the support of the project IDAWAS, DPI2009-11591 of the Direccion General de Investigacion del Ministerio de Ciencia e Innovacion (Spain), with the supplementary support of ACOMP/2011/188 of the Conselleria d'Educacio of the Generalitat Valenciana, and the support given to the first author by Spanish project MTM2010-18539. The third author is also indebted to the Universitat Politecnica de Valencia for the sabbatical leave granted during the first semester of 2011. The use of English in this paper was revised by John Rawlins.Benítez López, J.; Delgado Galván, XV.; Izquierdo Sebastián, J.; Pérez García, R. (2012). An approach to AHP decision in a dynamic context. Decision Support Systems. 53(3):499-506. https://doi.org/10.1016/j.dss.2012.04.015S49950653

Towards secure judgments aggregation in AHP

In the decision making methods the common assumption is the honesty and professionalism of experts. However, this is not the case when one or more experts in the group decision making framework, such as the group analytic hierarchy process (GAHP), try to manipulate results in their favor. The aim of this paper is to introduce two heuristics in the GAHP setting allowing to detect the manipulators and minimize their effect on the group consensus by diminishing their weights. The first heuristic is based on the assumption that manipulators will provide judgments which can be considered outliers with respect to judgments of the rest of the experts in the group. Second heuristic assumes that dishonest judgments are less consistent than average consistency of the group. Both approaches are illustrated with numerical examples and simulations.Comment: 32 page

Efficiency Analysis of Simple Perturbed Pairwise Comparison Matrices

Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the latter’s components is at least as close to the corresponding element of the pairwise comparison matrix as the one of the former’s components is, and the latter’s approximation is strictly better in at least one position. A pairwise comparison matrix is called simple perturbed if it differs from a consistent pairwise comparison matrix in one element and its reciprocal. One of the classical weighting methods, the eigenvector method is analyzed. It is shown in the paper that the principal right eigenvector of a simple perturbed pairwise comparison matrix is efficient. An open problem is exposed: the search for a necessary and sufficient condition of that the principal right eigenvector is efficient

Consistency test and weight generation for additive interval fuzzy preference relations

Some simple yet pragmatic methods of consistency test are developed to check whether an interval fuzzy preference relation is consistent. Based on the definition of additive consistent fuzzy preference relations proposed by Tanino (Fuzzy Sets Syst 12:117–131, 1984), a study is carried out to examine the correspondence between the element and weight vector of a fuzzy preference relation. Then, a revised approach is proposed to obtain priority weights from a fuzzy preference relation. A revised definition is put forward for additive consistent interval fuzzy preference relations. Subsequently, linear programming models are established to generate interval priority weights for additive interval fuzzy preference relations. A practical procedure is proposed to solve group decision problems with additive interval fuzzy preference relations. Theoretic analysis and numerical examples demonstrate that the proposed methods are more accurate than those in Xu and Chen (Eur J Oper Res 184:266–280, 2008b)

A methodology for implementing the analytical hierarchy process to decision-making in mining

A research report submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment for the degree of Master of Science in Engineering Johannesburg 2015The Analytic Hierarchy Process (AHP) is a Multi Criteria Decision-Making (MCDM) tool, which has gained wide acceptance in all disciplines in science and engineering. Although it has been used in mining engineering applications, it is only recently gaining significant momentum in the mining industry. Given its simplicity, it may seem surprising that it has not received wide acceptance, but this is probably due to a lack of both publicity and a user-friendly methodology. This report introduces a simple methodology that can be employed by anyone who possesses basic knowledge of arithmetic and spreadsheets, without having to know or understand fully the mathematics that the process is based on.MT201

An overview on managing additive consistency of reciprocal preference relations for consistency-driven decision making and Fusion: Taxonomy and future directions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The reciprocal preference relation (RPR) is a powerful tool to represent decision makers’ preferences in decision making problems. In recent years, various types of RPRs have been reported and investigated, some of them being the ‘classical’ RPRs, interval-valued RPRs and hesitant RPRs. Additive consistency is one of the most commonly used property to measure the consistency of RPRs, with many methods developed to manage additive consistency of RPRs. To provide a clear perspective on additive consistency issues of RPRs, this paper reviews the consistency measurements of the different types of RPRs. Then, consistency-driven decision making and information fusion methods are also reviewed and classified into four main types: consistency improving methods; consistency-based methods to manage incomplete RPRs; consistency control in consensus decision making methods; and consistency-driven linguistic decision making methods. Finally, with respect to insights gained from prior researches, further directions for the research are proposed