In the context of healthcare systems, the performance evaluation of hospitals plays a crucial role in assessing the quality of healthcare systems and facilitating informed decision-making processes. However, the presence of data uncertainty poses significant challenges to accurate performance measurement. This paper presents a novel uncertain common-weights data envelopment analysis (UCWDEA) approach for evaluating the performance of hospitals under uncertain environments. The proposed UCWDEA approach addresses the limitations of traditional data envelopment analysis (DEA) models by incorporating the uncertainty theory (UT) to model the inherent uncertainty in input and output data. Also, by utilizing a common set of weights (CSW) technique, the UCWDEA method provides a more robust and reliable assessment of hospital performance. The main advantages of the proposed UCWDEA approach can be succinctly summarized as follows. Firstly, it allows for the comparison of all hospitals on a consistent basis to calculate a realistic efficiency score, rather than an overly optimistic efficiency score. Secondly, the uncertain common-weights DEA approach exhibits linearity, enhancing its applicability. Thirdly, it possesses the capability to extend its utility under various other prevalent uncertainty distributions. Moreover, it enhances the discriminatory power of results, facilitates the ranking of hospitals in the presence of data uncertainty, and aids in identifying the sensitivity and stability levels of hospitals towards data uncertainty. Notably, in order to showcase the pragmatic application and efficacy of the uncertain common-weights DEA model, a genuine dataset has been utilized to evaluate the efficiency of 20 public hospitals in Tehran, all of which are affiliated with the Iran University of Medical Sciences. The results of the experiment demonstrate the efficacy of the UCWDEA approach in assessing and ranking hospitals amidst uncertain conditions. In summary, the research outcomes can offer policymakers valuable insights regarding hospital performance amidst data uncertainty. Additionally, it can provide practical recommendations on optimizing resource allocation, benchmarking performance, and formulating effective policies to augment the overall efficiency and effectiveness of healthcare services.

Measuring the similarity between two trajectories is fundamental and essential for the similarity-based remaining useful life (RUL) prediction. Most previous methods do not adequately account for the epistemic uncertainty caused by asynchronous sampling, while others have strong assumption constraints, such as limiting the positional deviation of sampling points to a fixed threshold, which biases the results considerably. To address the issue, an uncertain ellipse model based on the uncertain theory is proposed to model the location of sampling points as an observation drawn from an uncertain distribution. Based on this, we propose a novel and effective similarity measure metric for any two degradation trajectories. Then, the Stacked Denoising Autoencoder (SDA) model is proposed for RUL prediction, in which the models can be first trained on the most similar degradation data and then fine-tuned by the target dataset. Experimental results show that the predictive performance of the new method is superior to prior methods based on edit distance on real sequence (EDR), longest common subsequence (LCSS), or dynamic time warping (DTW) and is more robust at different sampling rates.

As with probability theory, uncertainty theory has been developed, in recent years, to portray indeterminacy phenomena in various application scenarios. We are concerned, in this paper, with the convergence property of state trajectories to equilibrium states (or fixed points) of time delayed uncertain cellular neural networks driven by the Liu process. By applying the classical Banach\'s fixed-point theorem, we prove, under certain conditions, that the delayed uncertain cellular neural networks, concerned in this paper, have unique equilibrium states (or fixed points). By carefully designing a certain Lyapunov-Krasovskii functional, we provide a convergence criterion, for state trajectories of our concerned uncertain cellular neural networks, based on our developed Lyapunov-Krasovskii functional. We demonstrate under our proposed convergence criterion that the existing equilibrium states (or fixed points) are exponentially stable almost surely, or equivalently that state trajectories converge exponentially to equilibrium states (or fixed points) almost surely. We also provide an example to illustrate graphically and numerically that our theoretical results are all valid. There seem to be rare results concerning the stability of equilibrium states (or fixed points) of neural networks driven by uncertain processes, and our study in this paper would provide some new research clues in this direction. The conservatism of the main criterion obtained in this paper is reduced by introducing quite general positive definite matrices in our designed Lyapunov-Krasovskii functional.

A new variance formula is developed using the generalized inverse of an increasing function. Based on the variance formula, a new entropy formula for any uncertain variable is provided. Most of the entropy formulas in the literature are special cases of the new entropy formula. Using the new entropy formula, the maximum entropy distribution for unimodel entropy of uncertain variables is provided without using the Euler-Lagrange equation.

Responding to the social, economic, and environmental call to resolve current sustainability challenges, the concern about carbon dioxide emission reduction should be incorporated into the power investment decision process. Reflecting the low carbon emission requirement, this paper proposes a new optimization model for power project portfolio selection that simultaneously considers both of carbon emission trading scheme and carbon tax imposition. In this model, the initial investment outlay, the power sale price, the carbon trading price, and carbon tax rate are treated as uncertain variables considering the fast-changing environment and complex market situation. Incorporating the constraint on whether the carbon quota is exceeded into the model, two investment strategies are proposed for investors. Using the proposed model, the impact of the rises in carbon trading price and carbon tax rate on the investor\'s investment strategy selection and the carbon emission is simulated and analyzed through a case study. When the expected carbon price is 203.50 RMB/tCO2-eq or less, a company should invest based on the strategy that annual emissions exceed the quota to obtain a maximum expected NPV which is larger than 408588 million RMB. When future carbon prices are 352.00, 500.50 and 649.00 RMB/tCO2-eq, the government should impose carbon tax rates of 30, 30, and 40 RMB/tCO2 on a power company, respectively, to obtain carbon emission reduction effect. At last, to see the contrast effect of the results from simultaneous implementation of both carbon trading and carbon tax, the results considering the carbon trading alone or carbon tax alone are discussed, respectively.

Uncertain heat equation is a partial differential equation describing temperature changes with time, while the strength of heat source is affected by the interference of noise. This paper applies the three-dimensional uncertain heat equation in some practical problems, including average temperature, maximum temperature, minimum temperature and minimum time of reaching a given temperature by using mathematical tools of time integral, space integral, extreme value and first hitting time.

Enhanced index tracking problem is the issue of selecting a tracking portfolio to outperform the benchmark return with a minimum tracking error. In this paper, we address the enhanced index tracking problem based on uncertainty theory where stock returns are treated as uncertain variables instead of random variables. First, we propose a nonlinear uncertain optimization model, i.e., uncertain mean-absolute downside deviation enhanced index tracking model. Then, we give the analytical solution of the proposed optimization model when stock returns take linear uncertainty distributions. Based on the solution, we find that tracking portfolio frontier is a continuous curve composed of at most n - 1 different line segments. Furthermore, we give the condition that tracking portfolio return and risk increase with benchmark return and risk, respectively. Finally, we offer some experiments and show that our proposed model is effective in controlling the tracking error.

Traditional support vector machines (SVMs) play an important role in the classification of precise data. However, due to various reasons, available data are sometimes imprecise. In this paper, uncertain variables are adopted to describe the imprecise data, and an uncertain support vector machine (USVM) is built for linearly α -nonseparable sets based on soft margin method, where a penalty coefficient is utilized as the trade-off between the maximum margin and the sum of slack variables. Then the equivalent crisp model is derived based on the inverse uncertainty distributions. Numerical experiments are designed to illustrate the application of the soft margin USVM. Finally, metrics, such as accuracy, precision, and recall are used to evaluate the robustness of the proposed model.

In the field of graph theory, the shortest path problem is one of the most significant problems. However, since varieties of indeterminated factors appear in complex networks, determining of the shortest path from one vertex to another in complex networks may be a lot more complicated than the cases in deterministic networks. To illustrate this problem, the model of uncertain random digraph will be proposed via chance theory, in which some arcs exist with degrees in probability measure and others exist with degrees in uncertain measure. The main focus of this paper is to investigate the main properties of the shortest path in uncertain random digraph. Methods and algorithms are designed to calculate the distribution of shortest path more efficiently. Besides, some numerical examples are presented to show the efficiency of these methods and algorithms.

The outbreak of COVID-19 had a profound impact on the practice of university leadership in China. This study employs a case study as the research method, interviewing five Heads of the Departments from the Z University in China to examine the challenges to leadership in Chinese universities during the COVID-19 pandemic and explores effective countermeasures. Research findings reveal that the challenges they faced manifested in the government\'s closed management requirements and the students\' demands for freedom of entry and exit, the dynamic and flexible disciplinary development and the rigid teaching evaluation, and big data-enabled governance and the habit of human experience-oriented management. In response to these challenges, this study proposes suggestions for the Z University leaders in the post-pandemic era: establishing rules and regulations with a relaxed degree, tolerating ambiguity in online teaching, improving the ability of intelligent technology, and taking opportunities to learn.