Formulas to Calculate the Variance and Pseudo-Variance of Complex Uncertain Variable

Abstract

Uncertainty theory is a branch of mathematics that deals with human uncertainty, and uncertain variable is used to model an uncertain quantity. Uncertainty exists not only in real quantities but also in complex quantities. Complex uncertain variable is mainly used to model a complex uncertain quantity. In uncertainty theory, inverse uncertainty distribution provides an easy way to calculate expected value as well as variance of an uncertain variable. This paper proposes formulas to calculate variance and pseudo-variance via the inverse uncertainty distributions of the real and imaginary parts of a complex uncertain variable. Besides, inequalities about variance and pseudo-variance of a complex uncertain variable is also derived.