Article
An Extension to Deng’s Entropy in the Open
World Assumption with an Application in
Sensor Data Fusion
Yongchuan Tang
1,2,∗
ID
, Deyun Zhou
1
and Felix T. S. Chan
2,∗
1
School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, China;
dyzhou@nwpu.edu.cn
2
Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University,
Hong Kong, China
* Correspondence: tangyongchuan@mail.nwpu.edu.cn (Y.T.); f.chan@polyu.edu.hk (F.T.S.C.)
Received: 6 May 2018; Accepted: 8 June 2018; Published: 11 June 2018
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.
Keywords:
Dempster-Shafer evidence theory (DST); uncertainty measure; open world; closed world;
Deng entropy; extended belief entropy; sensor data fusion
1. Introduction
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
]. Uncertain information may
come from sensors with different credibilities and experts’s subjective judgement. The heterogeneous
sources and reliable degree increase the complexity and uncertainty of information process.
The Dempster-Shafer evidence theory (DST) [
12
,
13
] has a promising efficiency in uncertain information
processing such as information fusion [
14
,
15
]. However, there are still a few open issues in the DST
framework that need further study. Firstly, the approaches of managing the conflicting belief masses
still needs further refining [
16
,
17
]. Secondly, the reasonable ways of generating the mass functions for
the practical applications [
18
,
19
]. Thirdly, uncertainty quantification with the possible measures in
the DST framework [
20
,
21
], and the necessary properties a new belief entropy should obey [
22
–
24
].
Fourthly, rules of combining the body of evidence vary under different circumstances [
25
–
27
]. Inspired
Sensors 2018, 18, 1902; doi:10.3390/s18061902 www.mdpi.com/journal/sensors
