Fuyuan Xiao

Huaping He, Fuyuan Xiao

Dempster rule of combination (DRC) is widely used for uncertainty reasoning in intelligent information system, which is generalized to complex domain recently. However, as the increase of identification framework elements, the computational complexity of Dempster Rule of Combination increases exponentially. To address this issue, we propose a novel quantum Dempster rule of combination (QDRC) by means of Toffoli gate. The QDRC combination process is completely implemented using quantum circuits.

Tianxiang Zhan, Yuanpeng He, Hanwen Li et al.

Evidence theory is that the extension of probability can better deal with unknowns and inaccurate information. Uncertainty measurement plays a vital role in both evidence theory and probability theory. Approximate Entropy (ApEn) is proposed by Pincus to describe the irregularities of complex systems. The more irregular the time series, the greater the approximate entropy. The ApEn of the network represents the ability of a network to generate new nodes, or the possibility of undiscovered nodes. Through the association of network characteristics and basic probability assignment (BPA) , a measure of the uncertainty of BPA regarding completeness can be obtained. The main contribution of paper is to define the integrity of the basic probability assignment then the approximate entropy of the BPA is proposed to measure the uncertainty of the integrity of the BPA. The proposed method is based on the logical network structure to calculate the uncertainty of BPA in evidence theory. The uncertainty based on the proposed method represents the uncertainty of integrity of BPA and contributes to the identification of the credibility of BPA.

Fuyuan Xiao

In this paper, we generalize the belief function on complex plane from another point of view. We first propose a new concept of complex mass function based on the complex number, called complex basic belief assignment, which is a generalization of the traditional mass function in Dempster-Shafer evidence theory. On the basis of the de nition of complex mass function, the belief function and plausibility function are generalized. In particular, when the complex mass function is degenerated from complex numbers to real numbers, the generalized belief and plausibility functions degenerate into the traditional belief and plausibility functions in DSE theory, respectively.

Fuyuan Xiao

In this paper, an evidential distance measure is proposed which can measure the difference or dissimilarity between complex basic belief assignments (CBBAs), in which the CBBAs are composed of complex numbers. When the CBBAs are degenerated from complex numbers to real numbers, i.e., BBAs, the proposed distance will degrade into the Jousselme et al.'s distance. Therefore, the proposed distance provides a promising way to measure the differences between evidences in a more general framework of complex plane space.

Fuyuan Xiao

Dempster-Shafer evidence theory has been widely used in various fields of applications, because of the flexibility and effectiveness in modeling uncertainties without prior information. However, the existing evidence theory is insufficient to consider the situations where it has no capability to express the fluctuations of data at a given phase of time during their execution, and the uncertainty and imprecision which are inevitably involved in the data occur concurrently with changes to the phase or periodicity of the data. In this paper, therefore, a generalized Dempster-Shafer evidence theory is proposed. To be specific, a mass function in the generalized Dempster-Shafer evidence theory is modeled by a complex number, called as a complex basic belief assignment, which has more powerful ability to express uncertain information. Based on that, a generalized Dempster's combination rule is exploited. In contrast to the classical Dempster's combination rule, the condition in terms of the conflict coefficient between the evidences K<1 is released in the generalized Dempster's combination rule. Hence, it is more general and applicable than the classical Dempster's combination rule. When the complex mass function is degenerated from complex numbers to real numbers, the generalized Dempster's combination rule degenerates to the classical evidence theory under the condition that the conflict coefficient between the evidences K is less than 1. In a word, this generalized Dempster-Shafer evidence theory provides a promising way to model and handle more uncertain information.

Fuyuan Xiao

Multi-sensor data fusion technology plays an important role in real applications. Because of the flexibility and effectiveness in modelling and processing the uncertain information regardless of prior probabilities, Dempster-Shafer evidence theory is widely applied in a variety of fields of information fusion. However, counter-intuitive results may come out when fusing the highly conflicting evidences. In order to deal with this problem, a novel method for multi-sensor data fusion based on a new generalised belief divergence measure of evidences is proposed. Firstly, the reliability weights of evidences are determined by considering the sufficiency and importance of the evidences. After that, on account of the reliability weights of evidences, a new Generalised Belief Jensen-Shannon divergence (GBJS) is designed to measure the discrepancy and conflict degree among multiple evidences, which can be utilised to measure the support degrees of evidences. Afterwards, the support degrees of evidences are used to adjust the bodies of the evidences before using the Dempster's combination rule. Finally, an application in fault diagnosis demonstrates the validity of the proposed method.