Assume an uncertain process follows an uncertain differential equation, and some realizations of this process are observed. Parameter estimation for the uncertain differential equation that fits the observed data as much as possible is a core problem in practice. This paper first presents a problem of initial value estimation for uncertain differential equations and proposes an estimation method. In addition, the method of moments is recast for estimating the time-varying parameters in uncertain differential equations. Using those techniques, a COVID-19 spread model based on uncertain differential equation is derived, and the zero-day of COVID-19 spread in China is inferred.

Data envelopment analysis (DEA) is widely used to estimate efficiency, particularly with respect to firm performance in economics. When the observed data are imprecise, as in the cases involving carbon emissions or social benefits, an uncertain DEA model can provide a reasonable solution. However, current uncertain DEA models only consider technical efficiency and not scale efficiency. This leads to information scarcity during decision making processes. Therefore, in this paper, we attempt to introduce an uncertain DEA model for scale efficiency evaluations using imprecise inputs and outputs. Additionally, we provide a sensitivity and stability analysis of the uncertain DEA model for scale efficiency, and document a numerical example of the uncertain DEA model for scale efficiency.

One type of production problems is concerned with a sequence of production cycles in which the cycle time (i.e., the length of each cycle) and reward (e.g. production amount or cost) are characterized in terms of uncertain variables (not random variables). In order to deal with this problem, this paper proposes an uncertain production risk process. Moreover, the concepts of shortage index and shortage time of the uncertain production risk process are proposed, and the formulas for shortage index and the uncertainty distribution of shortage time are also derived. Finally, some numerical experiments are performed to illustrate the model and formulas.

In Bayesian rule an unknown parameter is thought to be a quantity whose variation can be characterized by a prior distribution. Then some data are observed from a population whose distribution function is indexed by the unknown parameter and then the prior distribution is updated according to the observed data. The updated prior distribution is named as the posterior distribution. Based on uncertainty theory, this paper first makes a connection between posterior uncertainty distribution and likelihood function, and proposes a new method to obtain the posterior uncertainty distribution from the prior uncertainty distribution with given observed data. Some examples with special uncertainty distributions are employed to explain the calculation. Furthermore, an uncertain urn problem is provided to illustrate the application of the new method.