Abstract
Quantification of uncertain degree in the Dempster-Shafer evidence theory (DST) framework with belief entropy is still an open issue, even a blank field for the open world assumption. Currently, the existed uncertainty measures in the DST framework are limited to the closed world where the frame of discernment (FOD) is assumed to be complete. To address this issue, this paper focuses on extending a belief entropy to the open world by considering the uncertain information represented as the FOD and the nonzero mass function of the empty set simultaneously. An extension to Deng’s entropy in the open world assumption (EDEOW) is proposed as a generalization of the Deng’s entropy and it can be degenerated to the Deng entropy in the closed world wherever necessary. In order to test the reasonability and effectiveness of the extended belief entropy, an EDEOW-based information fusion approach is proposed and applied to sensor data fusion under uncertainty circumstance. The experimental results verify the usefulness and applicability of the extended measure as well as the modified sensor data fusion method. In addition, a few open issues still exist in the current work: the necessary properties for a belief entropy in the open world assumption, whether there exists a belief entropy that satisfies all the existed properties, and what is the most proper fusion frame for sensor data fusion under uncertainty.
Highlights
Uncertain information processing plays a key role in complex systems of many fields such as sensor networks [1,2], pattern recognition [3,4], decision-making [5,6], supply chain network management [7,8], complex network [9] and target tracking [10,11]
Inspired by some research works, especially for the concept of the open world in [28,29,30], we argue that the uncertainty measure in the open world should be different from that in the closed world because the circumstance of uncertainty is different
It should be noticed that a few open issues still exist in the current work, for example, (1) what are the necessary properties for a belief entropy in the open world assumption; (2) whether there exists a belief entropy that satisfies all the existingproperties in the closed world; and (3) what is the proper fusion frame for sensor data fusion under uncertainty
Summary
Uncertain information processing plays a key role in complex systems of many fields such as sensor networks [1,2], pattern recognition [3,4], decision-making [5,6], supply chain network management [7,8], complex network [9] and target tracking [10,11]. It should be noticed that a few open issues still exist in the current work, for example, (1) what are the necessary properties for a belief entropy in the open world assumption; (2) whether there exists a belief entropy that satisfies all the existingproperties in the closed world; and (3) what is the proper fusion frame for sensor data fusion under uncertainty. This rest of this paper is organized as follows.
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