Uncertain logic is a generalization of classical logic for dealing with uncertain knowledge via uncertainty theory. The truth value is defined as the uncertain measure that a proposition is true. In this paper, a numerical method for calculating the truth value of uncertain formulas is proposed and some examples are presented. 2011 Elsevier Ltd. All rights reserved.

This paper addresses the issue of measuring similarity between pieces of uncertain information in the framework of possibility theory. In a first part, natural properties of such functions are proposed and a survey of the few existing measures is presented. Then, a new measure so-called Information Affinity is proposed to overcome the limits of the existing ones. The proposed function is based ...

This paper is concerned with an abstract formulation of stochastic optimal control systems, in which uncertainty is described by a relative entropy constraint between the nominal measure and the uncertain measure, while the payoff is a functional of the uncertain measure. This is a minimax game in which the controller seeks to minimize the pay-off, while the disturbance described by a set of me...

By confining the parametera in confident threshold 1 2 1 a £ < in rough set model based on uncertain measure, variable precision rough set model based on uncertain measure is given. The lower approximation and upper approximation are defined in approximation uncertainty space, and their properties are discussed. © 2011 World Academic Press, UK. All rights reserved.

In addition to the four axioms of uncertainty theory, this paper presents the fifth axiom called product measure axiom. This paper also gives an operational law of independent uncertain variables and a concept of entropy of continuous uncertain variables. Based on the uncertainty theory, a new uncertain calculus is proposed and applied to uncertain differential equation, finance, control, filte...

Entropy is used as a quantitative measurement of the information deficiency. In uncertain set theory, logarithm entropy for uncertain set has been proposed. However, it fails to measure the degree of uncertainty associated with some uncertain sets. Thus this paper will propose sine entropy for uncertain set as a supplement, and investigate its properties such as translation invariance and posit...

Uncertainty theory is a mathematical methodology for dealing withnon-determinate phenomena in nature. As we all know, uncertainprocess and uncertain integral are important contents of uncertaintytheory, so it is necessary to have deep research. This paperpresents the definition and discusses some properties of strongcomonotonic uncertain process. Besides, some useful formulas ofuncertain integr...

Uncertain differential equation with jumps, as a crucial tool to deal with a discontinuous uncertain system, is a type of differential equation driven by both canonical Liu process and uncertain renewal process. So far, a concept of stability in measure for an uncertain differential equation with jumps has been proposed. As a supplement, this paper proposes a concept of almost sure stability fo...

In this paper, problems of stability in measure and optimal control are considered for an uncertain continuous-time singular system which can be described by uncertain differential equations. Singular system is assumed to be regular and impulse-free. Under some given assumptions, the existence and uniqueness of the solution, and stability in measure of the singular system are presented. Then, b...

We introduce the fuzzy measure as a unifying structure for modeling knowledge about an uncertain variable. We show that a large class of well established types of uncertainty representation can be modeled in this framework. A measure of entropy associated with a fuzzy measure is introduced and its manifestation for different fuzzy measures is described. The problem of uncertain decision making ...