Entropies of uncertain random variables are introduced to provide some kinds of quantitative measurement of the uncertainty. In chance theory, a concept of entropy for uncertain random variables has been defined by using logarithm. However, such an entropy fails to measure the uncertain degree of some uncertain random variables. For solving this problem, this paper firstly define the elliptic e...

Over the past decade, the civil engineering community has ever more realized the importance and perspective of the reliability-based design optimization (RBDO), the selection of a design that satisfies performance constraints with a specified probability. Since then several stochastic simulation algorithms for computing small failure probabilities encountered in reliability analysis of engineer...

Over the past decade, the civil engineering community has ever more realized the importance and perspective of reliability-based design optimization (RBDO). Since then several advanced stochastic simulation algorithms for computing small failure probabilities encountered in reliability analysis of engineering systems have been developed: Subset Simulation (Au and Beck (2001) [2]), Line Sampling...

Clustering on uncertain data, one of the essential tasks in mining uncertain data, posts significant challenges on both modeling similarity between uncertain objects and developing efficient computational methods. The previous methods extend traditional partitioning clustering methods like k-means and density-based clustering methods like DBSCAN to uncertain data, thus rely on geometric distanc...

Uncertain variable is used to model quantities in uncertainty. This paper considers comonotonic functions of an uncertain variable, and gives their uncertainty distributions. Besides, it proves the linearity of expected value operator on comonotonic functions of an uncertain variable.

Multistage stochastic programming is a key technology for making decisions over time in an uncertain environment. One of the promising areas in which this technology is implementable, is medium term planning of electricity production and trading where decision makers are typically faced with uncertain parameters (such as future demands and market prices) that can be described by stochastic proc...

A large chunk of probability is about random variables. Instead of giving a precise definition, let us just mention that a random variable can be thought of as an uncertain, numerical (i.e., with values in R) quantity. While it is true that we do not know with certainty what value a random variable X will take, we usually know how to assign a number the probability that its value will be in som...

Uncertain random variables are used to describe the phenomenon of simultaneous appearance of both uncertainty and randomness in a complex system. For modeling multi-objective decision-making problems with uncertain random parameters, a class of uncertain random optimization is suggested for decision systems in this paper, called the uncertain random multi-objective programming. For solving the ...

A fractional minimal cost flow problem under linear type belief degree based uncertainty is studied for the first time. This type of uncertainty is useful when no historical information of an uncertain event is available. The problem is crisped using an uncertain chance-constrained programming approach and its non-linear objective function is linearized by a variable changing approach. An illus...