The ordered weighted averaging (OWA) operators play a crucial role in aggregating multiple criteria evaluations into an overall assessment supporting the decision makers’ choice. One key point steps is to determine the associated weights. In this paper, we first briefly review some main methods for determining the weights by using distribution functions. Then we propose a new approach for determining OWA weights by using the regular increasing monotone quantifier. Motivated by the idea of normal distribution‐based method to determine the OWA weights, we develop a method based on elliptical distributions for determining the OWA weights, and some of its desirable properties have been investigated.
In order to fully consider the decision-maker’s limited rationality and attitude to risk, this paper constructs the probabilistic hesitant fuzzy TOPSIS emergency decision-making model based on the cumulative prospect theory under the probabilistic hesitant fuzzy environment. Aiming at the problem of missing probabilistic information in the probabilistic hesitant fuzzy element, a new complement scheme is proposed. In this scheme, the weighted average result of the original data information is used to complement, and the original data information is retained to a large extent. Then this paper proposes several probabilistic hesitant fuzzy distance measures based on Lance distance. The decision reference point is constructed by the probabilistic hesitant fuzzy Lance distance, which overcomes the influence of the extreme value on the decision-making result, and defines the value function based on the probability hesitation fuzzy Lance distance. In view of the fact that the attribute weights are completely unknown, the probabilistic hesitant fuzzy exponential entropy is constructed by using the actual data, and the attribute weights of different prospect states are obtained. Aiming at the problem that attribute weights of different prospect states have different effects on the cumulative prospect value, the expression of the cumulative prospect value is improved. The improved closeness coefficient of the TOPSIS method is used to order the emergency schemes. Finally, the new method is applied to the emergency decision-making case of a sudden outbreak of epidemic respiratory disease. The results show that the contrast of the new method is obvious, which is conducive to distinguish different schemes. The new method is more suitable for the complex and changeable emergency decision-making field.
We propose a simple new index, named the CI-index, based on the Choquet integral to characterize the scientific output of researchers. This index is an improvement of the A-index and R-index and has a notable feature that highly cited papers have highly weights and lowly cited papers have lowly weights. We proposed a ranking method of distinguish researchers to compare their scientific outputs. In applications many researchers may have the same h-index, g-index or R-index, however, the CI-index can be provided an effective method of distinguish among such researchers.
We introduce a new broad and flexible class of multivariate elliptically symmetric distributions including the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied, including the distribution of linear transformations, marginal distributions, conditional distributions, moments, stochastic representations and characteristic function.
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