In multiple-criteria decision making/aiding/analysis (MCDM/MCDA) weights of criteria constitute a crucial input for finding an optimal solution (alternative). A large number of methods were proposed for criteria weights derivation including direct ranking, point allocation, pairwise comparisons, entropy method, standard deviation method, and so on. However, the problem of correct criteria weights setting persists, especially when the number of criteria is relatively high. The aim of this paper is to approach the problem of determining criteria weights from a different perspective: we examine what weights’ values have to be for a given alternative to be ranked the best. We consider a space of all feasible weights from which a large number of weights in the form ofn−tuples is drawn randomly via Monte Carlo method. Then, we use predefined dominance relations for comparison and ranking of alternatives, which are based on the set of generated cases. Further on, we provide the estimates for a sample size so the results could be considered robust enough. At last, but not least, we introduce the concept ofcentral weightsand the measure of its robustness (stability) as well as the concept of alternatives’multi-dominance, and show their application to a real-world problem of the selection of the best wind turbine.

We forecast 1,000,000 COVID-19 cases outside of China by March 31st, 2020 based on a heuristic and WHO situation reports. We do not model the COVID-19 pandemic; we model only the number of cases.

In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we apply One-Factor-At-a-Time (OFAT) sensitivity analysis via Monte Carlo simulations; the number of compared objects ranges from 3 to 8, and the comparison scale coincides with Saaty’s fundamental scale from 1 to 9 with reciprocals. Our findings suggest that the BWM is, on average, significantly more sensitive statistically (and thus less robust) and more susceptible to order violation than the GMM and EVM for every examined matrix (vector) size, even after adjustment for the different numbers of pairwise comparisons required by each method. On the other hand, differences in sensitivity and order violation between the GMM and EMM were found to be mostly statistically insignificant.

Pairwise comparisons constitute a popular and important tool for multiple-criteria decision making. Consistency is one particular aspect of pairwise comparisons that has been studied thoroughly in recent decades since human judgements are seldom fully consistent. The aim of this paper is to propose a new simple and intuitive iterative Step-by-Step (SBS) algorithm for inconsistency reduction of a (multiplicative) pairwise comparison matrix based on step-by-step changes of the most inconsistent matrix element, where the inconsistency is measured by a modified Koczkodaj’s inconsistency index. A comparison of the proposed SBS algorithm with other algorithms for inconsistency reduction is provided as well.