On the Monte Carlo weights in multiple criteria decision analysis.

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 of n-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 of central weights and 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.

The evaluation of COVID-19 prediction precision with a Lyapunov-like exponent.

In the field of machine learning, building models and measuring their performance are two equally important tasks. Currently, measures of precision of regression models' predictions are usually based on the notion of mean error, where by error we mean a deviation of a prediction from an observation. However, these mean based measures of models' performance have two drawbacks. Firstly, they ignore the length of the prediction, which is crucial when dealing with chaotic systems, where a small deviation at the beginning grows exponentially with time. Secondly, these measures are not suitable in situations where a prediction is made for a specific point in time (e.g. a date), since they average all errors from the start of the prediction to its end. Therefore, the aim of this paper is to propose a new measure of models' prediction precision, a divergence exponent, based on the notion of the Lyapunov exponent which overcomes the aforementioned drawbacks. The proposed approach enables the measuring and comparison of models' prediction precision for time series with unequal length and a given target date in the framework of chaotic phenomena. Application of the divergence exponent to the evaluation of models' accuracy is demonstrated by two examples and then a set of selected predictions of COVID-19 spread from other studies is evaluated to show its potential.

The law of demand and the loss of confidence effect: An experimental study.

The aim of this article is to examine the possibility that a market demand function (curve) might not be monotonically decreasing in its entire domain according to the consumer theory neoclassical as assumed by the law of demand (for normal goods). This may happen due to limited rationality of (some) consumers and the anchor price effect. When a price of a good decreases to some point, the amount demanded might stops increasing due to the loss of confidence effect: consumers' unwillingness to buy a too cheap product. The existence of this effect was examined via questionnaire on a sample of 377 undergraduate university students from the Czech Republic, Ecuador and Spain. The main result of this experimental study is that the loss of confidence effect appeared at all three locations, which indicates that the law of demand may not be valid in its entire domain. Furthermore, the results of this study imply that a significant percentage of people make decisions of limited rationality even when facing a very simple task. In addition, statistically significant difference in rational behavior with respect to gender was found.