Abstract
Dempster-Shafer evidence theory has wide applications in many fields. Recently, A new entropy called Deng entropy was proposed in evidence theory. Some scholars have pointed out that Deng Entropy does not satisfy the additivity in uncertain measurements. However, irreducibility may have a huge effect. The derived entropy from complex systems is often irreducible. Inspired by this, generalized belief entropy is proposed. The belief entropy implies the relationship between Deng entropy, Renyi entropy, Tsallis entropy. In addition, numerical examples demonstrate the flexibility of the proposed Renyi-Deng (R-D) entropy to measure the uncertainty of basic probability assignment (BPA). Finally, a method for identifying contradictory evidence based on Renyi-Deng (R-D) entropy is proposed. The experiment show the effectiveness of the proposed method.
Highlights
Dempster-Shafer theory of evidence [1], [2] was proposed by Dempster [1] and developed by Shafer et al [2]
Rényi entropy and Tsallis entropy respectively generalized to quasi-linear means and non-extensive systems [57], while Deng entropy comes from evidence theory based on power set
Our contributions are to propose generalized Deng entropies which reveal the relationship among Deng entropy, Rényi entropy and Tsallis entropy
Summary
Dempster-Shafer theory of evidence [1], [2] was proposed by Dempster [1] and developed by Shafer et al [2]. Evidence theory as a framework of uncertain reasoning is closely related to probability theory. It can be considered as a generalization of probability, assigning belief to power set of the propositions rather than single elements. Maeda and Ichihashi [31] propose an uncertain measurement method This uncertainty consists of two types, one containing the uncertainty of Shannon entropy. A new entropy named Deng entropy [32] has been proposed to solve uncertain measurement. This entropy is directly related to basic probability assignment. A method based on Rényi-Deng (R-D) entropy to identify contradictory evidence is proposed.
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