In order to deal with a system with both randomness and uncertainty, chance theory has been built, and uncertain random variable has been proposed as a generalization of random variable and uncertain variable. Correspondingly, as a generalization of both stochastic process and uncertain process, this paper will propose an uncertain random process. In addition, some special types of uncertain ra...

It is generally assumed in the traditional formulation of supervised learning that only the outputs data are uncertain. However, this assumption might be too strong for some learning tasks. This paper investigates the use of Gaussian Process prior to infer consistent models given uncertain data. By assuming a Gaussian distribution with known variances over the inputs and a Gaussian covariance f...

We consider repeated games where the number of repetitions θ is unknown. The information about the uncertain duration can change during the play of the game. This is described by an uncertain duration process that defines the probability law of the signals that players receive at each stage about the duration. To each repeated game and uncertain duration process is associated the -repeated game...

Uncertain renewal process is an important uncertain process. This paper discusses some sample properties of uncertain renewal process. Besides, it gives some theorems on first hitting time of renewal process.

Uncertain calculus deals with the integral and differential of some uncertain processes. So far, uncertain integrals have been defined with respect to Liu process, renewal process, finite variation process, and multiple Liu processes. This paper presents an uncertain integral of a matrix of uncertain processes with respect to multi-dimensional Liu process, and verifies its linearity property. T...

This paper investigates the design of nonlinear controllers for process plant applications that could be modeled by relatively low order uncertain dynamics, such as industrial processes (e.g. level, flow, pressure, etc.) and also some automotive applications (e.g. active suspension). The design technique is based on using a combination of state feedback and Lyapunov-based techniques. The key is...

Delayed renewal process and delayed renewal reward process are introduced in the framework of uncertainty theory and their uncertainty distributions are provided. Furthermore, delayed renewal theorem on the limit value of the expected renewal rate of the process and delayed renewal reward theorem on the limit value of the long-run expected reward per unit time are presented. At last, some examp...

Uncertain process is initialized for modelling the evolution of uncertain phenomena. An uncertain process is said to have independent increments if its increments are independent uncertain variables whenever the time intervals do not overlap, and have stationary increments if its increments are identically distributed uncertain variables whenever the time intervals have the same length. Then st...

This paper proves the fundamental theorem of uncertain calculus with respect to both canonical process and renewal process, which gives the differential of an uncertain process in the form of a function of canonical process and renewal process.

The production planning is an important problem in most of manufacturing systems in practice. Unlike many researches existing in literature, this problem encounters with great uncertainties in parameters and input data. In this paper, a single machine capacitated production planning problem is considered and a linear programming formulation is presented. The production costs are assumed to be u...