The Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices

The paper presents the Triads Geometric Consistency Index (T-GCI), a measure for evaluating the inconsistency of the pairwise comparison matrices employed in the Analytic Hierarchy Process (AHP). Based on the Saaty''s definition of consistency for AHP, the new measure works directly with triads of the initial judgements, without having to previously calculate the priority vector, and therefore is valid for any prioritisation procedure used in AHP. The T-GCI is an intuitive indicator defined as the average of the log quadratic deviations from the unit of the intensities of all the cycles of length three. Its value coincides with that of the Geometric Consistency Index (GCI) and this allows the utilisation of the inconsistency thresholds as well as the properties of the GCI when using the T-GCI. In addition, the decision tools developed for the GCI can be used when working with triads (T-GCI), especially the procedure for improving the inconsistency and the consistency stability intervals of the judgements used in group decision making. The paper further includes a study of the computational complexity of both measures (T-GCI and GCI) which allows selecting the most appropriate expression, depending on the size of the matrix. Finally, it is proved that the generalisation of the proposed measure to cycles of any length coincides with the T-GCI. It is not therefore necessary to consider cycles of length greater than three, as they are more complex to obtain and the calculation of their associated measure is more difficult

AHP-group decision making based on consistency

The Precise consistency consensus matrix (PCCM) is a consensus matrix for AHP-group decision making in which the value of each entry belongs, simultaneously, to all the individual consistency stability intervals. This new consensus matrix has shown significantly better behaviour with regards to consistency than other group consensus matrices, but it is slightly worse in terms of compatibility, understood as the discrepancy between the individual positions and the collective position that synthesises them. This paper includes an iterative algorithm for improving the compatibility of the PCCM. The sequence followed to modify the judgments of the PCCM is given by the entries that most contribute to the overall compatibility of the group. The procedure is illustrated by means of its application to a real-life situation (a local context) with three decision makers and four alternatives. The paper also offers, for the first time in the scientific literature, a detailed explanation of the process followed to solve the optimisation problem proposed for the consideration of different weights for the decision makers in the calculation of the PCCM

Pairwise comparison matrices and the error-free property of the decision maker

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal

Assessing Value-based Health Care Delivery for Hemodialysis

Rationale, aims and objectives Disparities in haemodialysis outcomes among centres have been well-documented. Besides, attempts to assess haemodialysis results have been based on non-comprehensive methodologies. This study aimed to develop a comprehensive methodology for assessing haemodialysis centres, based on the value of health care. The value of health care is defined as the patient benefit from a specific medical intervention per monetary unit invested (Value = Patient Benefit/Cost). This study assessed the value of health care and ranked different haemodialysis centres. Method A nephrology quality management group identified the criteria for the assess- ment. An expert group composed of stakeholders (patients, clinicians and managers) agreed on the weighting of each variable, considering values and preferences. Multi-criteria methodology was used to analyse the data. Four criteria and their weights were identified: evidence-based clinical performance measures = 43 points; yearly mortality = 27 points; patient satisfaction = 13 points; and health-related quality of life = 17 points (100-point scale). Evidence-based clinical performance measures included five sub-criteria, with respective weights, including: dialysis adequacy; haemoglobin concentration; mineral and bone disorders; type of vascular access; and hospitalization rate. The patient benefit was determined from co-morbidity–adjusted results and corresponding weights. The cost of each centre was calculated as the average amount expended per patient per year. Results The study was conducted in five centres (1–5). After adjusting for co-morbidity, value of health care was calculated, and the centres were ranked. A multi-way sensitivity analysis that considered different weights (10–60% changes) and costs (changes of 10% in direct and 30% in allocated costs) showed that the methodology was robust. The rankings: 4-5-3-2-1 and 4-3-5-2-1 were observed in 62.21% and 21.55%, respectively, of simula- tions, when weights were varied by 60%. Conclusions Value assessments may integrate divergent stakeholder perceptions, create a context for improvement and aid in policy-making decisions

Analysis of pairwise comparison matrices: an empirical research

Pairwise comparison (PC) matrices are used in multi-attribute decision problems (MADM) in order to express the preferences of the decision maker. Our research focused on testing various characteristics of PC matrices. In a controlled experiment with university students (N = 227) we have obtained 454 PC matrices. The cases have been divided into 18 subgroups according to the key factors to be analyzed. Our team conducted experiments with matrices of different size given from different types of MADM problems. Additionally, the matrix elements have been obtained by different questioning procedures differing in the order of the questions. Results are organized to answer five research questions. Three of them are directly connected to the inconsistency of a PC matrix. Various types of inconsistency indices have been applied. We have found that the type of the problem and the size of the matrix had impact on the inconsistency of the PC matrix. However, we have not found any impact of the questioning order. Incomplete PC matrices played an important role in our research. The decision makers behavioral consistency was as well analyzed in case of incomplete matrices using indicators measuring the deviation from the final order of alternatives and from the final score vector

The rank reversal problem in multi-criteria decision making : a literature review

Despite the importance of multicriteria decision-making (MCDM) techniques for constructing effective decision models, there are many criticisms due to the occurrence of a problem called rank reversal. Nevertheless, there is a lack of a systematic literature review on this important subject which involves different methods. This study reviews the pertinent literature on rank reversal, based on 130 related articles published from 1980 to 2015 in international journals, which were gathered and analyzed according to the following perspectives: multicriteria technique, year and journal in which the papers were published, co-authorship network, rank reversal types, and research goal. Thus our survey provides recommendations for future research, besides useful information and knowledge regarding rank reversal in the MCDM field

A decision support system and visualisation tools for AHP-GDM

The Precise Consistency Consensus Matrix (PCCM) is a decisional tool for AHP-Group Decision Making (AHP-GDM). Based on the initial pairwise comparison matrices of the individuals, the PCCM constructs a consensus matrix for the group using the concept of consistency. This paper presents a decision support system (PRIOR-PCCM) that facilitates the construction of the PCCM in the context of AHP-GDM, and the calculus of four indicators that allows comparison of the behaviour of group consensus matrices. PRIOR-PCCM incorporates the possibility of considering different weights for the decision makers and includes a module that permits the extension of the initial PCCM which can achieve the minimum number of non-null entries required for deriving priorities or establishing a complete PCCM matrix. It also includes two cardinal indicators for measuring consistency and compatibility and two ordinal indicators for evaluating the number of violations of consistency and priority. The paper introduces some new visualisation tools that improve comprehension of the process followed for obtaining the PCCM matrix and allow the cognitive exploitation of the results. These original contributions are illustrated with a case study

Strategic Optimal Path and Developmental Environment on Photovoltaic Industry in China Based on an AHP-SWOT Hybrid Model

International audienceUtilizing the qualitative analysis of SWOT and quantitative method of AHP, this paper presented the AHP-SWOT hybrid model of the photovoltaic industry in China in order to calculate the influence of the strengths, weaknesses, opportunities & threats (SWOT factors and SWOT sub-factors), and the SO strategy, WO strategy, ST countermeasure and WT countermeasure on the development of the photovoltaic industry in China. The results show that the influence of the threats are the most, the weaknesses and opportunities second, and the strengths the least among four SWOT factors of the development of the photovoltaic industry in China. Thereby, among 12 SWOT sub-factors, complete industrial chains are the most important factor in the strengths factors, lack of core technology is of the most significance in the weaknesses factors, latent necessity of the photovoltaic industry development as a result of global energy crisis is the most valuable opportunities factor, and external trade environment deteriorating due to international trade protection is the most threats factor. Among four combination path of the development strategy, the WT countermeasure possesses the most valuable positive influences on the development of the photovoltaic industry in China, which is the optimal path for the strategy alternatives