A random variable is a measurable function from an uncertainty space to the set of real numbers, which is used to model randomness. An uncertain variable is a measurable function from uncertainty space to the set of real numbers, which is used to describe uncertainty. However, randomness and uncertainty often simultaneously appear in a complex system. Uncertain random variable provides a useful...

Planning with actions concurrency under resources and time uncertainty has been recognized as a challenging and interesting problem. Most current approaches rely on a discrete model to represent resources and time, which contributes to the combinatorial explosion of the search space when dealing with both actions concurrency and resources and time uncertainty. A recent alternative approach uses...

What does it take for real-deterministic $c$-valued (i.e., classical, commuting) variables to comply with the Heisenberg uncertainty principle? Here, we construct a class of out weak values obtained via nonperturbing measurement quantum operators postselection over complete set state vectors basis, which always satisfies Kennard-Robertson-Schr\"odinger relation. First, introduce an auxiliary gl...

We prove an uncertainty relation, which imposes a bound on any joint measurement of position and momentum. It is of the form (∆P )(∆Q) ≥ C~, where the ‘uncertainties’ quantify the difference between the marginals of the joint measurement and the corresponding ideal observable. Applied to an approximate position measurement followed by a momentum measurement, the uncertainties become the precisi...

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicted. Based on the notion of chance measure, a concept of uncertain random entropy is introduced and used to provide a quantitative measurement of the uncertainty associated with uncertain random variables and its properties are studied in this paper. Relative entropy is a measure of the differ...