Information volume of Z-number

Abstract

Given a probability distribution, Shannon entropy can be used to measure its corresponding information volume. However, it is still an open issue to calculate the information volume of Z-number. In this paper, the information volume of the Z-number is presented using the proposed transformation of a Z-number into a mass function. In our proposed method, the mass function degenerates into probability distribution under the circumstance that the uncertainty of the Z-restriction is 0. In this case, the information volume degenerates into Shannon entropy. The information volume of a given Z-number increases approximately linearly with the unreliability of its Z-restriction. In addition, the information volume varies with the value of Z-restriction and fuzzy number A. Some illustrative examples are shown to demonstrate the properties of the proposed information volume of Z-number. A new Weighted Multiple Attribute Decision Making (WMADM) method is also proposed to illustrate the practical advantage of the proposed information volume.