This paper first reviews different types of uncertainty. In order to construct fuzzy counterparts of Brownian motion and stochastic calculus, this paper proposes some basic concepts of fuzzy process, including fuzzy calculus and fuzzy differential equation. Those new concepts are also extended to hybrid process and uncertain process. A basic stock model is presented, thus opening up a way to fu...

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.