Uncertain delay differential equation is a type of differential equations driven by a canonical Liu process. This paper mainly focuses on the stability of uncertain delay differential equations. At first, the concept of stability in measure, stability in mean and stability in moment for uncertain delay differential equations will be presented. In addition, the sufficient condition for uncertain...

This paper focuses on the stability of multifactor uncertain differential equation. The stability for the solution of multifactor uncertain differential equation is investigated, including stability in measure and stability in mean. Some stability theorems for the solution of such type of uncertain differential equation are given, in which some sufficient conditions for a multifactor uncertain ...

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicted. Based on the notion of chance measure, a concept of uncertain random entropy is introduced and used to provide a quantitative measurement of the uncertainty associated with uncertain random variables and its properties are studied in this paper. Relative entropy is a measure of the differ...

Generalized trapezoidal fuzzy numbers (GTFNs) have been widely applied in uncertain decision-making problems. The similarity between GTFNs plays an important part in solving such problems, while there are some limitations in existing similarity measure methods. Thus, based on the cosine similarity, a novel similarity measure of GTFNs is developed which is combined with the concepts of geometric...

High-order uncertain differential equations are applied to model differentiable uncertain systems with high-order differentials. In order to describe the influence of the initial value on the solution, this paper proposes two concepts of stability for high-order uncertain differential equation, including stability in measure and stability in mean. Most important of all, some stability theorems ...

In this paper, the knapsack problem under uncertain environment is investigated, in which the weights and the values are assumed to be uncertain variables. With different criteria, three mathematical models are constructed for the problem, i.e., expected value model, chance-constrained programming model and uncertain measure model. Taking advantage of uncertainty theory, the first two models ca...

Clustering is an unsupervised classification technique for grouping set of abstract objects into classes of similar objects. Clustering uncertain data is one of the essential tasks in mining uncertain data. Uncertain data is typically found in the area of sensor networks, weather data, customer rating data etc. The earlier methods for clustering uncertain data based on probability distribution,...

In recent times, intuitionistic fuzzy sets introduced by Atanassov has been one of the most powerful and flexible approaches for dealing with complex and uncertain situations of real world. In particular, the concept of divergence between intuitionistic fuzzy sets is important since it has applications in various areas such as image segmentation, decision making, medical diagnosis, pattern reco...

Uncertain objects, where each feature is represented by multiple observations or a given or fitted probability density function, arise in applications such as sensor networks, moving object databases and medical and biological databases. We propose a methodology to classify uncertain objects based on a new probabilistic distance measure between an uncertain object and a group of uncertain objec...