Axiomatization of Inconsistency Indicators for Pairwise Comparisons

This study proposes revised axioms for defining inconsistency indicators in pairwise comparisons. It is based on the new findings that "PC submatrix cannot have a worse inconsistency indicator than the PC matrix containing it" and that there must be a PC submatrix with the same inconsistency as the given PC matrix. This study also provides better reasoning for the need of normalization. It is a revision of axiomatization by Koczkodaj and Szwarc, 2014 which proposed axioms expressed informally with some deficiencies addressed in this study.Comment: This paper should have been withdrawn by the first author a long time ago. The work has been finished with another researcher, I have been pushed out the projec

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

A characterization of the Logarithmic Least Squares Method

We provide an axiomatic characterization of the Logarithmic Least Squares Method (sometimes called row geometric mean), used for deriving a preference vector from a pairwise comparison matrix. This procedure is shown to be the only one satisfying two properties, correctness in the consistent case, which requires the reproduction of the inducing vector for any consistent matrix, and invariance to a specific transformation on a triad, that is, the weight vector is not influenced by an arbitrary multiplication of matrix elements along a 3-cycle by a positive scalar.Comment: 11 page

The triangle assessment method: a new procedure for eliciting expert judgement

The Analytic Hierarchy Process (AHP) is one of the most widely used Multi-Criteria Decision-Making methods worldwide. As such, it is subject to criticisms that highlight some potential weaknesses. In this study, we present a new Multi-Criteria Decision-Making method denominated the “Triangular Assessment Method” (referred to by its Spanish abbreviation, MTC©). The MTC© aims to make use of the potential of AHP while avoiding some of its drawbacks. The main characteristics and advantages of the MTC© can be summarised as follows: (i) evaluation of criteria, and of the alternative options for each criterion, in trios instead of pairs; (ii) elimination of discrete scales and values involved in judgements; (iii) a substantial reduction in the number of evaluations (trios) relative to the corresponding number of pairs which would have to be considered when applying the AHP method; (iv) consistent decision-making; (v) introduction of closed cyclical series for comparing criteria and alternatives; and (vi) the introduction of opinion vectors and opinion surfaces. This new method is recommended for supporting decision-making with large numbers of subjective criteria and/or alternatives and also for group decisions where the consensus must be evaluated. The MTC© provides a different promising perspective in decision-making and could lead to new research lines in the field of information systems.This work was supported by the Galician Regional Government [“Programa de Consolidación e Estructuración de Unidades de Investigación Competitivas, modalidade de Grupos de Referencia Competitiva” for the period 2006–2017] and by the European Union [ERDF program]. Likewise, the authors thank Daniele de Rigo, Dora Henriques and Cesar Pérez-Cruzado, because his comments improved notably this manuscript.info:eu-repo/semantics/publishedVersio

Methodological quality of network meta-analysis in dentistry : a meta-research

This meta-research aimed to provide an overview of the methodological quality and risk of bias of network meta-analyses (NMA) in dentistry. Searches for NMA of randomized clinical trials with clinical outcomes in dentistry were performed in databases up to January 2022. Two reviewers independently screened titles/ abstracts, selected full texts, and extracted the data. The adherence to PRISMA-NMA reporting guideline, the AMSTAR-2 methodological quality tool, and the ROBIS risk of bias tool were assessed in the studies. Correlation between the PRISMA-NMA adherence and the AMSTAR-2 and ROBIS results was also investigated. Sixty-two NMA studies were included and presented varied methodological quality. According to AMSTAR-2, half of the NMA presented moderate quality (n = 32; 51.6%). The adherence to PRISMA-NMA also varied. Only 36 studies (58.1%) prospectively registered the protocol. Other issues lacking of reporting were data related were data related to the NMA geometry and the assessment of results consistency, and the evaluation of risk of bias across the studies. ROBIS assessment showed a high risk of bias mainly for domains 1 (study eligibility criteria) and 2 (identification and selection of studies). Correlation coefficients between the PRISMA-NMA adherence and the AMSTAR-2 and ROBIS results showed moderate correlation (rho < 0.6). Overall, NMA studies in dentistry were of moderate quality and at high risk of bias in several domains, especially study selection. Future reviews should be better planned and conducted and have higher compliance with reporting and quality assessment tools

Optimization for Decision Making II

In the current context of the electronic governance of society, both administrations and citizens are demanding the greater participation of all the actors involved in the decision-making process relative to the governance of society. This book presents collective works published in the recent Special Issue (SI) entitled “Optimization for Decision Making II”. These works give an appropriate response to the new challenges raised, the decision-making process can be done by applying different methods and tools, as well as using different objectives. In real-life problems, the formulation of decision-making problems and the application of optimization techniques to support decisions are particularly complex and a wide range of optimization techniques and methodologies are used to minimize risks, improve quality in making decisions or, in general, to solve problems. In addition, a sensitivity or robustness analysis should be done to validate/analyze the influence of uncertainty regarding decision-making. This book brings together a collection of inter-/multi-disciplinary works applied to the optimization of decision making in a coherent manner

Simplified models for multi-criteria decision analysis under uncertainty

Includes abstract.Includes bibliographical references.When facilitating decisions in which some performance evaluations are uncertain, a decision must be taken about how this uncertainty is to be modelled. This involves, in part, choosing an uncertainty format {a way of representing the possible outcomes that may occur. It seems reasonable to suggest {and is an aim of the thesis to show {that the choice of how uncertain quantities are represented will exert some influence over the decision-making process and the final decision taken. Many models exist for multi-criteria decision analysis (MCDA) under conditions of uncertainty; perhaps the most well-known are those based on multi-attribute utility theory [MAUT, e.g. 147], which uses probability distributions to represent uncertainty. The great strength of MAUT is its axiomatic foundation, but even in its simplest form its practical implementation is formidable, and although there are several practical applications of MAUT reported in the literature [e.g. 39, 270] the number is small relative to its theoretical standing. Practical applications often use simpler decision models to aid decision making under uncertainty, based on uncertainty formats that `simplify' the full probability distributions (e.g. using expected values, variances, quantiles, etc). The aim of this thesis is to identify decision models associated with these `simplified' uncertainty formats and to evaluate the potential usefulness of these models as decision aids for problems involving uncertainty. It is hoped that doing so provides some guidance to practitioners about the types of models that may be used for uncertain decision making. The performance of simplified models is evaluated using three distinct methodological approaches {computer simulation, `laboratory' choice experiments, and real-world applications of decision analysis {in the hope of providing an integrated assessment. Chapter 3 generates a number of hypothetical decision problems by simulation, and within each problem simulates the hypothetical application of MAUT and various simplified decision models. The findings allow one to assess how the simplification of MAUT models might impact results, but do not provide any general conclusions because they are based on hypothetical decision problems and cannot evaluate practical issues like ease-of-use or the ability to generate insight that are critical to good decision aid. Chapter 4 addresses some of these limitations by reporting an experimental study consisting of choice tasks presented to numerate but unfacilitated participants. Tasks involved subjects selecting one from a set of five alternatives with uncertain attribute evaluations, with the format used to represent uncertainty and the number of objectives for the choice varied as part of the experimental design. The study is limited by the focus on descriptive rather than real prescriptive decision making, but has implications for prescriptive decision making practice in that natural tendencies are identified which may need to be overcome in the course of a prescriptive analysis

Filling Key Gaps in Population and Community Ecology

We propose research to fill key gaps in the areas of population and community ecology, based on a National Science Foundation workshop identifying funding priorities for the next 5–10 years. Our vision for the near future of ecology focuses on three core areas: predicting the strength and context-dependence of species interactions across multiple scales; identifying the importance of feedbacks from individual interactions to ecosystem dynamics; and linking pattern with process to understand species coexistence. We outline a combination of theory development and explicit, realistic tests of hypotheses needed to advance population and community ecology

Methodological quality of network meta-analysis in dentistry: a meta-research

This meta-research aimed to provide an overview of the methodological quality and risk of bias of network meta-analyses (NMA) in dentistry. Searches for NMA of randomized clinical trials with clinical outcomes in dentistry were performed in databases up to January 2022. Two reviewers independently screened titles/abstracts, selected full texts, and extracted the data. The adherence to PRISMA-NMA reporting guideline, the AMSTAR-2 methodological quality tool, and the ROBIS risk of bias tool were assessed in the studies. Correlation between the PRISMA-NMA adherence and the AMSTAR-2 and ROBIS results was also investigated. Sixty-two NMA studies were included and presented varied methodological quality. According to AMSTAR-2, half of the NMA presented moderate quality (n = 32; 51.6%). The adherence to PRISMA-NMA also varied. Only 36 studies (58.1%) prospectively registered the protocol. Other issues lacking of reporting were data related were data related to the NMA geometry and the assessment of results consistency, and the evaluation of risk of bias across the studies. ROBIS assessment showed a high risk of bias mainly for domains 1 (study eligibility criteria) and 2 (identification and selection of studies). Correlation coefficients between the PRISMA-NMA adherence and the AMSTAR-2 and ROBIS results showed moderate correlation (rho < 0.6). Overall, NMA studies in dentistry were of moderate quality and at high risk of bias in several domains, especially study selection. Future reviews should be better planned and conducted and have higher compliance with reporting and quality assessment tools