An LP-based inconsistency monitoring of pairwise comparison matrices

A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The results can be applied in the process of filling in the matrix as the decision maker gets automatic feedback. As soon as a serious error occurs among the matrix elements, even due to a misprint, a significant increase in the inconsistency index is reported. The high inconsistency may be alarmed not only at the end of the process of filling in the matrix but also during the completion process. Numerical examples are also provided

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

Inconsistency thresholds for incomplete pairwise comparison matrices

Pairwise comparison matrices are increasingly used in settings where some pairs are missing. However, there exist few inconsistency indices for similar incomplete data sets and no reasonable measure has an associated threshold. This paper generalises the famous rule of thumb for the acceptable level of inconsistency, proposed by Saaty, to incomplete pairwise comparison matrices. The extension is based on choosing the missing elements such that the maximal eigenvalue of the incomplete matrix is minimised. Consequently, the well-established values of the random index cannot be adopted: the inconsistency of random matrices is found to be the function of matrix size and the number of missing elements, with a nearly linear dependence in the case of the latter variable. Our results can be directly built into decision-making software and used by practitioners as a statistical criterion for accepting or rejecting an incomplete pairwise comparison matrix

Multi-Factor Triage Algorithm (MUFTA): Quantitative and Qualitative Ethical Factors on Triage Decisions During COVID-19

Background: This study shows how multiple ethical criteria evaluations result in patient screening and ranking. Furthermore, as Omicron outbreaks increase, hospital emergency departments will become overburdened with critically ill patients. It is a one-of-a-kind global triage algorithm for infectious decreases of COVID-19 and Omicron. The algorithm is qualitative and quantitative, and adaptable to various bio-ethical and social factors. The measurement of the evaluation process eliminates any inconsistencies, which is an advantage of a decision-making algorithm. The proposed algorithm is unique because there are no similar algorithms in the literature that provide triage guidelines based on social ethics, bioethics, and human dignity. Objective: It's simple to evaluate a patient's potential benefits when ethical triage judgments are structured and transparent. Furthermore, decisions made primarily based on economic considerations in stressful situations overlook the socioeconomic realities of the underprivileged. This triage algorithm eliminates the need for ad hoc triage evaluations and facilitates criteria for inclusion, such as human dignity. It also takes into account patient comorbidities and social, ethical issues. Method: Healthcare professionals use predefined ethical criteria to assign relative rankings among patients based on treatment response and social circumstances. It is a Delphi method for evaluating patient illnesses with the help of medical professionals. For example, the admission to the intensive care unit and providing a ventilator depend entirely on hierarchical multidimensional triage scoring results. This algorithm can evaluate triage scores quickly. It is robust, accurate, and quick in assessment, evaluation, and reevaluation during an emergency. A team of three experts can implement this algorithm. Result: The Consistency Scores (CR) show how well clinical and non-clinical ethical criteria may be used to make triage judgments. As a result, all specialists have reported allogeneic reactions in the triage assessment. Furthermore, this system enables decision-makers to identify cognitive biases that may influence their decisions. A Group Consciousness Ratio (GCR) of over 85% indicates that the decision-making process is transparent. Patients with a high level of social dependency, a reasonable probability of recovery, a favorable weighted average comorbidity score, and those who are less fortunate are all considered in the overall triage decision. Conclusions: This algorithm differentiates patients who need ICU (Incentive Care Unit) care and do not immediately require critical resources. As a result, patients queue up on a waiting list when the ICU demand spikes due to the increased incidence of COVID-19 infection or its variants. This situation presents a dilemma for the triage policy. Therefore, a national emergency policy requires monetary and technical assistance to expand healthcare facilities. However, the clarity of this triage policymaking is at odds with decision-makers interested in manipulating results. It is challenging to deal with consistency issues in the Delphi process in group decision-making without professional moderators and valid evaluation metrics. Therefore, transparency, consistency, and strong judgment are essential elements of the presented algorithm. Doi: 10.28991/esj-2022-SPER-07 Full Text: PD