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...

Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Different from randomness and fuzziness, uncertainty theory provides a new mathematical model for uncertain phenomena. A key concept to describe uncertain quantity is uncertain variable, and expected value operator provides an average value of uncert...

Chance theory is put forward as a tool to deal with a complex system including randomness and uncertainty. As a fundamental concept in chance theory, uncertain random variable is an extension of random variable and uncertain variable. This paper obtains a new law of large numbers for independent uncertain random variables but not necessarily identically distributed.

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...

Uncertainty theory is a branch of axiomatic mathematics that deals with human uncertainty, and uncertain variable is used tomodel the uncertain quantities. Inverse uncertainty distribution provides an easy way to calculate the functions of uncertain variables as well as their expected values. This paper mainly presents a formula to calculate the variance of an uncertain variable via the inverse...

Estimating the prerequisite structure of skills is a crucial issue in domain modeling. Students usually learn skills in sequence since the preliminary skills need to be learned prior to the complex skills. The prerequisite relations between skills underlie the design of learning sequence and adaptation strategies for tutoring systems. The prerequisite structures of skills are usually studied by...

The classification of fuzzy uncertain data is considered one of the most challenging issues in data analysis. In spite of the significance of fuzzy data in mathematical programming, the development of the analytical methods of fuzzy data is slow. Therefore, the current study proposes a new fuzzy data classification method based on fuzzy data envelopment analysis (DEA) which can handle strea...

In many cases, human uncertainty and objective randomness simultaneously appear in a system. In order to describe this phenomena, this paper presents a new concept of uncertain random variable. To measure uncertain random events, this paper also combines probability measure and uncertain measure into a chance measure. Based on the tool of chance measure, the concepts of chance distribution, exp...