In this paper, several useful inequalities for uncertain variables are proved. A BorelCantelli lemma for uncertain measures is obtained and some convergence theorems for continuous uncertain measures are derived. Finally, these theorems are applied to compute the uncertainty distribution of Liu integral. We prove that the uncertain integral of a deterministic function with respect to a Liu proc...

Multi-dimensional uncertain differential equation is a system of uncertain differential equations driven by amulti-dimensional Liu process. This paper first gives the analytic solutions of two special types of multi-dimensional uncertain differential equations. After that, it proves that the multi-dimensional uncertain differential equation has a unique solution provided that its coefficients s...

In designing and developing large complex products, people use models to describe and organize interrelated elements in both product systems (architecture, use cases, constraints...) and process systems (activities, deliverables, roles...). However, exchanged information is often incomplete, vague and not entirely determined at the beginning of the project and during its evolution. Our project ...

With the evolution of technology, the ways to acquire data and the applications of data are more diverse. As data volume continuously grows, the data quality may not be high as usual. The data can be defected, imprecise or inaccurate due to the process of data acquiring. Recently, the skyline query is widely used in data analysis to derive the results that meets more than one specific condition...

Learning with uncertain inputs is well-known to be a difficult task. In order to achieve this analytically using a Gaussian Process prior model, we expand the original process around the input mean (Delta method), assuming the random input is normally distributed. We thus derive a new process whose covariance function accounts for the randomness of the input. We illustrate the effectiveness of ...

The steadily increasing need for optimal operation of plants and processes with respect to economic and ecological requirements has led to a manifold of research efforts in the field of real-time optimization (RTO) of uncertain process systems. Recent advances on RTO include conditions guaranteeing plant optimality upon convergence based on first-order modification of the optimization problem; ...

In this paper, firstly, one deals with the stability and the stabilizability problems for the class of Markovian jump continuous-time singular systems. Next, one will address the robustness problem. The proposed approaches derive sufficient conditions such that the regularity and the absence of impulses are assured as well as the stochastic stability and robust stochastic stability. Also, state...

This paper presents a systematic methodology for building causal models that can be used for fault detection and isolation. The aim of a causal model is to capture the influences between the variables of a continuous process and to generate qualitative and quantitative knowledge that is interpreted by a diagnostic module. Following a model-based approach for fault detection, the diagnostic modu...

We consider the problem of multi-step ahead prediction in time series analysis using the non-parametric Gaussian process model. k-step ahead forecasting of a discrete-time nonlinear dynamic system can be performed by doing repeated one-step ahead predictions. For a state-space model of the form yt = f(yt−1, . . . , yt−L), the prediction of y at time t + k is based on the estimates ŷt+k−1, . . ....

Uncertain field is virtually an extension of uncertain process with the index space changing from a totally ordered set into a partially ordered one such as time-space or a surface. For describing the uncertain field, this paper introduces several concepts of uncertainty distribution and inverse uncertainty distribution. In addition, a sufficient and necessary condition is proved for the uncert...