Characterisation of the consistent completion of AHP comparison matrices using graph theory

[EN] Decision-making is frequently affected by uncertainty and/or incomplete information, which turn decision-making into a complex task. It is often the case that some of the actors involved in decision-making are not sufficiently familiar with all of the issues to make the appropriate decisions. In this paper, we are concerned about missing information. Specifically, we deal with the problem of consistently completing an analytic hierarchy process comparison matrix and make use of graph theory to characterize such a completion. The characterization includes the degree of freedom of the set of solutions and a linear manifold and, in particular, characterizes the uniqueness of the solution, a result already known in the literature, for which we provide a completely independent proof. Additionally, in the case of nonuniqueness, we reduce the problem to the solution of nonsingular linear systems. In addition to obtaining the priority vector, our investigation also focuses on building the complete pairwise comparison matrix, a crucial step in the necessary process (between synthetic consistency and personal judgement) with the experts. The performance of the obtained results is confirmed.Benítez López, J.; Carpitella, S.; Certa, A.; Izquierdo Sebastián, J. (2019). Characterisation of the consistent completion of AHP comparison matrices using graph theory. Journal of Multi-Criteria Decision Analysis. 26(1-2):3-15. https://doi.org/10.1002/mcda.1652S315261-2Benítez, J., Carrión, L., Izquierdo, J., & Pérez-García, R. (2014). Characterization of Consistent Completion of Reciprocal Comparison Matrices. Abstract and Applied Analysis, 2014, 1-12. doi:10.1155/2014/349729Benítez, J., Delgado-Galván, X., Gutiérrez, J. A., & Izquierdo, J. (2011). Balancing consistency and expert judgment in AHP. 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Comparative analysis of MCDM methods for the assessment of sustainable housing affordability

While affordability is traditionally assessed in economic terms, this paper tests a new assessment method that draws closer links with sustainability by considering economic, social and environmental criteria that impact on a household's quality of life. The paper presents an empirical application and comparison of six different multiple criteria decision making (MCDM) approaches for the purpose of assessing sustainable housing affordability.The comparative performance of the weighted product model (WPM), the weighted sum model (WSM), the revised AHP, TOPSIS and COPRAS, is investigated. The purpose of the comparative analysis is to determine how different MCDM methods compare when used for a sustainable housing affordability assessment model. 20 Evaluative criteria and 10 alternative are as in Liverpool, England, were considered. The applicability of different MCDM methods for the focused decision problem was investigated. The paper discusses the similarities in MCDM methods, evaluates their robustness and contrasts the resulting rankings

Joint stakeholder decision-making on the management of the Silao-Romita aquifer using AHP

Over-exploitation and pollution have been identified as the main problems facing the Silao-Romita aquifer in Guanajuato, Mexico. The objective of this paper is to analyze the current situation, characterized by a clear lack of legislative enforcement, dispersion of competences, and scarcity of economic resources, in order to establish a new prioritization of action plans, and choose from among three specific management options. One of the main challenges when addressing these problems in a holistic manner is the conflicting viewpoints of the sectors involved. As each stakeholder has a different perception, there is a clear need for appropriate mechanisms to reach a consensus in decision-making. To achieve the objective, we use the Analytic Hierarchy Process (AHP), because of its flexibility and the availability of mathematical axiomatic principles and techniques to obtain group preferences and priorities. In addition, we use several tools developed by the authors to obtain consistency, streamline the trade-off between stakeholder know-how and synthetic consistency, and consistently complete partial judgments given by some of the stakeholders. The problem of obtaining a consensus among the actors involved regarding criteria and alternatives is also considered. The obtained results are intended to serve as guidelines for conducting priority actions to help solve the general problem of the study area, and to identify the management model that best meets the needs of the aquifer, according to the actors involved. (C) 2013 Elsevier Ltd. All rights reserved.This work has been supported by project IDAWAS, DPI2009-11591 of the Spanish Ministry of Science and Innovation; with supplementary support from ACOMP/2011/188 of the education department of the Generalitat Valenciana. The first author wishes to thank CONACYT for the 10007-2011-01 scholarship program. The use of English in this paper was revised by John Rawlins.Delgado Galván, XV.; Izquierdo Sebastián, J.; Benítez López, J.; Pérez García, R. (2014). Joint stakeholder decision-making on the management of the Silao-Romita aquifer using AHP. Environmental Modelling & Software. 51:310-322. https://doi.org/10.1016/j.envsoft.2013.10.008S3103225

A mixed-data evaluation in group TOPSIS with differentiated decision power

[[abstract]]This main objective of this paper is to provide decision support for mixed data in group Technique for Order Preference by Similarity to Idea Solution (TOPSIS) with differentiated decision power. We use a signum function to compare the ordinal performance of alternatives on any qualitative criterion, or the partial information provided by decision makers. The proposed process for ordinal information is uniformly coherent with the traditional TOPSIS steps, preserving the characteristic of distance-based utilities. Ordinal weights are also considered herein, and the decision power of the group members is formulated by their weights under an agreement in the group. Two examples demonstrate that the proposed approach has some benefits and achieves robustness with two types of sensitivity analyses. Some discussions and their limitations to the approach are also provided.[[notice]]補正完

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