In this paper, we define a measure of robustness for a set of parameterized transfer functions as delivered by classical prediction error identification and that contains the true system at a prescribed probability level. This measure of robustness is the worst case Vinnicombe distance between the model and the plants in the uncertainty region. We show how it can be computed exactly using LMI-b...

In the three-layered framework for knowledge discovery, it is necessary for technique layer to develop some data-driven algorithms, whose knowledge acquiring process is characterized by and hence advantageous for the unnecessity of prior domain knowledge or external information. System uncertainty is able to conduct data-driven knowledge acquiring process. It is crucial for such a knowledge acq...

The idea of representing choice under uncertainty as a trade-off between mean returns and some measure of risk or uncertainty is fundamental to the analysis of investment decisions. In this paper, we show that preferences can be characterized in this way, even in the absence of objective probabilities. We develop a model of uncertainty averse preferences that is based on a mean and a measure of...

Ranking methods, similarity measures and uncertainty measures are very important concepts for interval type-2 fuzzy sets (IT2 FSs). So far, there is only one ranking method for such sets, whereas there are many similarity and uncertainty measures. A new ranking method and a new similarity measure for IT2 FSs are proposed in this paper. All these ranking methods, similarity measures and uncertai...

In managing business processes, the process uncertainty and variability are significant factors causing difficulties in prediction and decision making, which evokes and augments the importance and need of process measures for systematic analysis. We propose an entropy-based process measure to quantify the uncertainty of business process models. The proposed measure enables capturing the dynamic...

In this note, we argue that the axiomatic requirement of range to the measure of aggregated total uncertainty (ATU) in Dempster-Shafer theory is not reasonable.

In this work, we consider a recently proposed entropy I (called varentropy) defined by a variational relationship ) ( dx x d dI − = β as a measure of uncertainty of random variable x. By definition, varentropy underlies a generalized virtual work principle 0 = dx leading to maximum entropy 0 ) ( = − x I d β . This paper presents an analytical investigation of this maximizable entropy for severa...

New position uncertainty (delocalization) measures for a particle on the circle are proposed and illustrated on several examples, where the previous measures (based on 2π-periodic position operators) appear to be unsatisfactory. The new measures are suitably constructed using the standard multiplication angle operator variances. They are shown to depend solely on the state of the particle and t...

Shannnon entropy is an efficient tool to measure uncertain information. However, it cannot handle the more uncertain situation when the uncertainty is represented by basic probability assignment (BPA), instead of probability distribution, under the framework of Dempster Shafer evidence theory. To address this issue, a new entropy, named as Deng entropy, is proposed. The proposed Deng entropy is...

We develop a new approach to formulate and prove the weak uncertainty inequality, which was recently introduced by Okoudjou and Strichartz. We assume either an appropriate measure growth condition with respect to the effective resistance metric, or, in the absence of such a metric, we assume the Poincaré inequality and reverse volume doubling property. We also consider the weak uncertainty ineq...