Partial entropy is a measure to characterize how much of entropy of an uncertain random variable belongs to uncertain variables. In this paper, a definition of partial quadratic entropy of uncertain random variables is proposed. Furthermore, some properties of partial quadratic entropy are derived such as positive linearity. c ©2016 World Academic Press, UK. All rights reserved.

In recent years, uncertain data has become ubiquitous because of new technologies for collecting data which can only measure and collect the data in an imprecise way. Furthermore, many technologies such as privacy-preserving data mining create data which is inherently uncertain in nature. As a result there is a need for tools and techniques for mining and managing uncertain data. This chapter d...

An uncertain random variable is a measurable function from a probability space to the set of uncertain variables. In this paper, subadditivity property of chance measure and some inequalities on expected value for uncertain random variables including Jensen’s Inequality, Liapunov Inequality and cp Inequality are proved. Based on these inequalities, linear property and other properties of conver...

In recent years, uncertain data has become ubiquitous because of new technologies for collecting data which can only measure and collect the data in an imprecise way. Furthermore, many technologies such as privacy-preserving data mining create data which is inherently uncertain in nature. As a result there is a need for tools and techniques for mining and managing uncertain data. This chapter d...

In this paper, an uncertain version of Borel-Cantelli lemma is proved. Besides, some convergence theorems of continuous uncertain measure are proposed. Using these theorems, it is proved that the uncertainty distribution function of the uncertain integral on a real function is a normal one.

Complex uncertain variables are measurable functions from an uncertainty space to the set of complex numbers and are used to model complex uncertain quantities. This paper introduces the convergence concepts of complex uncertain sequences: convergence almost surely (a.s.), convergence in measure, convergence in mean, convergence in distribution and convergence uniformly almost surely. In additi...

Entropy is a measure of the uncertainty associated with an uncertain variable. So far, entropy, quadratic entropy and sine entropy have been proposed for uncertain variables. This paper will propose a triangular entropy for uncertain variables, and verify its properties such as translation invariance and positive linearity.

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...

In recent years, uncertain data has become ubiquitous because of new technologies for collecting data which can only measure and collect the data in an imprecise way. Furthermore, many technologies such as privacy-preserving data mining create data which is inherently uncertain in nature. As a result there is a need for tools and techniques for mining and managing uncertain data. This chapter d...

Data Mining is the extraction of hidden predictive information from large databases. Clustering is one of the popular data mining techniques. 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 p...