Abstract
Quantifying uncertainty is a hot topic for uncertain information processing in the framework of evidence theory, but there is limited research on belief entropy in the open world assumption. In this paper, an uncertainty measurement method that is based on Deng entropy, named Open Deng entropy (ODE), is proposed. In the open world assumption, the frame of discernment (FOD) may be incomplete, and ODE can reasonably and effectively quantify uncertain incomplete information. On the basis of Deng entropy, the ODE adopts the mass value of the empty set, the cardinality of FOD, and the natural constant e to construct a new uncertainty factor for modeling the uncertainty in the FOD. Numerical example shows that, in the closed world assumption, ODE can be degenerated to Deng entropy. An ODE-based information fusion method for sensor data fusion is proposed in uncertain environments. By applying it to the sensor data fusion experiment, the rationality and effectiveness of ODE and its application in uncertain information fusion are verified.
Highlights
The Open Deng entropy (ODE) takes into account the sources of uncertain information in the Dempster–Shafer evidence theory framework that are rarely considered by other existing methods, including the uncertain information brought by the incomplete frame of discernment (FOD) and the non-zero mass function of empty set
Step 2: use Open Deng entropy to measure the uncertain information of BPA before further processing the data, it is necessary to use a reasonable and applicable uncertainty measure to measure the uncertainty of the information modeled by BPA in step 1
An uncertainty measurement method that is based on Deng entropy named ODE
Summary
Uncertain information processing is applied to complex systems in many fields, such as sensor networks [1,2], pattern recognition [3,4], and supply chain network management [5,6]. Belief entropy has shown its advantages for addressing uncertain information processing in some practical applications, such as risk analysis [36,37,38], decision-making [15,33] and sensor data fusion [39]. An improved belief entropy named Open Deng entropy (ODE) is proposed in this work in order to solve the uncertainty measurement of open world assumption. The ODE takes into account the sources of uncertain information in the Dempster–Shafer evidence theory framework that are rarely considered by other existing methods, including the uncertain information brought by the incomplete FOD and the non-zero mass function of empty set.
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