相关论文: Representation of Uncertainty for Limit Processes

This paper investigates fuzzy nonlinear system equations using an optimization approach. Here, the inner-outer direct search technique is used with fuzzy coefficients and vectors to quantify the uncertain solution. The fuzzy nonlinear…

This paper studies the propagation of finite-sample uncertainty under nonlinear transformations commonly used in statistical decision systems. In particular, we consider process capability indices, which are widely used in manufacturing…

Proper quantification and propagation of uncertainties in computational simulations are of critical importance. This issue is especially challenging for CFD applications. A particular obstacle for uncertainty quantifications in CFD problems…

We introduce a general theory of epistemic random fuzzy sets for reasoning with fuzzy or crisp evidence. This framework generalizes both the Dempster-Shafer theory of belief functions, and possibility theory. Independent epistemic random…

This paper presents a fuzzy system approach to the prediction of nonlinear time-series and dynamical systems. To do this, the underlying mechanism governing a time-series is perceived by a modified structure of a fuzzy system in order to…

Methods for analyzing or learning from "fuzzy data" have attracted increasing attention in recent years. In many cases, however, existing methods (for precise, non-fuzzy data) are extended to the fuzzy case in an ad-hoc manner, and without…

The problem of developing models and algorithms for multilevel association mining pose for new challenges for mathematics and computer science. These problems become more challenging, when some form of uncertainty like fuzziness is present…

Reliable corner detection is an important task in determining the shape of different regions within an image. Real-life image data are always imprecise due to inherent uncertainties that may arise from the imaging process such as…

Data-driven modeling is useful for reconstructing nonlinear dynamical systems when the underlying process is unknown or too expensive to compute. Having reliable uncertainty assessment of the forecast enables tools to be deployed to predict…

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…

This paper introduces the notion of fuzzy process as a formalism for the idea of fuzzy contact between a device and its environment. The notions of absolute correctness and relative correctness are defined. In order to work with concurrency…

This paper develops a smooth model identification and self-learning strategy for dynamic systems taking into account possible parameter variations and uncertainties. We have tried to solve the problem such that the model follows the changes…

This paper mainly focuses on (1) a generalized treatment of fuzzy sets of type $n$, where $n$ is an integer larger than or equal to $1$, with an example, mathematical discussions, and real-life interpretation of the given mathematical…

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterise uncertainty in model inputs and how…

We propose a novel foundation for calculus that focuses on the notion of approximations while avoiding the use of limits altogether. Continuity is defined as approximation at a point, while differentiability is defined as approximation with…

The modeling and uncertainty quantification of closed curves is an important problem in the field of shape analysis, and can have significant ramifications for subsequent statistical tasks. Many of these tasks involve collections of closed…

Modeling human ratings data subject to raters' decision uncertainty is an attractive problem in applied statistics. In view of the complex interplay between emotion and decision making in rating processes, final raters' choices seldom…

In many time-dependent problems of practical interest the parameters entering the equations describing the evolution of the various quantities exhibit uncertainty. One way to address the problem of how this uncertainty impacts the solution…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…