Z-number is a new framework of fuzzy sets that combines with constraint and reliability. Managing the uncertainty of Z-number is an important issue in the fuzzy decision making of Z-number based. In this paper, we first develop a new uncertainty measure of fuzzy set considering the influence of fuzziness measure and the range (or cardinality) of the fuzzy set. Some properties of the developed uncertainty measure of the fuzzy set are presented. We then propose and discuss method of measuring the uncertainty of Z-number. Examples are used to illustrate the effectiveness of the proposed methodologies.

How to manage the uncertainty of the basic probability assignment accurately and efficiently is of significance and also an open issue. Plenty of functions have been established to cover the issue, especially Deng entropy recently. Deng entropy can deal with the more complex situation of the focal elements (propositions). However, Deng entropy has some limitations when the propositions are of the intersection. In this paper, a modified function is proposed by considering the scale of the frame of discernment and the influence of the intersection between statements on uncertainty. The proposed belief entropy provides a promising way to measure the uncertain information. Some numerical examples and an application in pattern recognition are used to show the efficiency and accuracy of the proposed belief entropy.

Sensor data fusion plays an important role in fault diagnosis. Dempster–Shafer (D-R) evidence theory is widely used in fault diagnosis, since it is efficient to combine evidence from different sensors. However, under the situation where the evidence highly conflicts, it may obtain a counterintuitive result. To address the issue, a new method is proposed in this paper. Not only the statistic sensor reliability, but also the dynamic sensor reliability are taken into consideration. The evidence distance function and the belief entropy are combined to obtain the dynamic reliability of each sensor report. A weighted averaging method is adopted to modify the conflict evidence by assigning different weights to evidence according to sensor reliability. The proposed method has better performance in conflict management and fault diagnosis due to the fact that the information volume of each sensor report is taken into consideration. An application in fault diagnosis based on sensor fusion is illustrated to show the efficiency of the proposed method. The results show that the proposed method improves the accuracy of fault diagnosis from 81.19% to 89.48% compared to the existing methods.