Information volume of Z-number (Q6195471)

A discrete Z-number \(X = (A,B)\) describing an uncertain variable \(X\) is a pair of fuzzy numbers \(A\), \(B\) where \(A\) is a fuzzy description of possible values of the variable and \(B\) is a fuzzy probability measure of \(A\). Here, a transformation of discrete Z-numbers to a probability mass function is presented and an information volume of Z-numbers based on this transformation is proposed. Numerical examples show that when the information source is certain (uncertainty = \(0\)) the mass function generated from a Z-number degenerates into a probability distribution. Greater unreliability of the Z-restriction of a Z-number leads to greater information volume, the relationship is approximately linear; an example demonstrates the application of the proposed methods in weighted multiple attribute decision-making where opinions of experts are represented using Z-numbers.