A New Correlation Measure for Belief Functions and Their Application in Data Fusion
Measuring the correlation between belief functions is an important issue in Dempster–Shafer theory. From the perspective of uncertainty, analyzing the correlation may provide a more comprehensive reference for uncertain information processing. However, existing studies about correlation have not com...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-06-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/25/6/925 |
| _version_ | 1797594922204790784 |
|---|---|
| author | Zhuo Zhang Hongfei Wang Jianting Zhang Wen Jiang |
| author_facet | Zhuo Zhang Hongfei Wang Jianting Zhang Wen Jiang |
| author_sort | Zhuo Zhang |
| collection | DOAJ |
| description | Measuring the correlation between belief functions is an important issue in Dempster–Shafer theory. From the perspective of uncertainty, analyzing the correlation may provide a more comprehensive reference for uncertain information processing. However, existing studies about correlation have not combined it with uncertainty. In order to address the problem, this paper proposes a new correlation measure based on belief entropy and relative entropy, named a belief correlation measure. This measure takes into account the influence of information uncertainty on their relevance, which can provide a more comprehensive measure for quantifying the correlation between belief functions. Meanwhile, the belief correlation measure has the mathematical properties of probabilistic consistency, non-negativity, non-degeneracy, boundedness, orthogonality, and symmetry. Furthermore, based on the belief correlation measure, an information fusion method is proposed. It introduces the objective weight and subjective weight to assess the credibility and usability of belief functions, thus providing a more comprehensive measurement for each piece of evidence. Numerical examples and application cases in multi-source data fusion demonstrate that the proposed method is effective. |
| first_indexed | 2024-03-11T02:29:33Z |
| format | Article |
| id | doaj.art-3556b20f95d74b80aaca6255ab4d5cee |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-11T02:29:33Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-3556b20f95d74b80aaca6255ab4d5cee2023-11-18T10:18:20ZengMDPI AGEntropy1099-43002023-06-0125692510.3390/e25060925A New Correlation Measure for Belief Functions and Their Application in Data FusionZhuo Zhang0Hongfei Wang1Jianting Zhang2Wen Jiang3School of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, ChinaSchool of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, ChinaNo. 91977 Unit of People’s Liberation Army of China, Beijing 100036, ChinaSchool of Electronics and Information, Northwestern Polytechnical University, Xi’an 710072, ChinaMeasuring the correlation between belief functions is an important issue in Dempster–Shafer theory. From the perspective of uncertainty, analyzing the correlation may provide a more comprehensive reference for uncertain information processing. However, existing studies about correlation have not combined it with uncertainty. In order to address the problem, this paper proposes a new correlation measure based on belief entropy and relative entropy, named a belief correlation measure. This measure takes into account the influence of information uncertainty on their relevance, which can provide a more comprehensive measure for quantifying the correlation between belief functions. Meanwhile, the belief correlation measure has the mathematical properties of probabilistic consistency, non-negativity, non-degeneracy, boundedness, orthogonality, and symmetry. Furthermore, based on the belief correlation measure, an information fusion method is proposed. It introduces the objective weight and subjective weight to assess the credibility and usability of belief functions, thus providing a more comprehensive measurement for each piece of evidence. Numerical examples and application cases in multi-source data fusion demonstrate that the proposed method is effective.https://www.mdpi.com/1099-4300/25/6/925Dempster–Shafer theorybelief correlation measureuncertaintyinformation fusionmulti-source data |
| spellingShingle | Zhuo Zhang Hongfei Wang Jianting Zhang Wen Jiang A New Correlation Measure for Belief Functions and Their Application in Data Fusion Entropy Dempster–Shafer theory belief correlation measure uncertainty information fusion multi-source data |
| title | A New Correlation Measure for Belief Functions and Their Application in Data Fusion |
| title_full | A New Correlation Measure for Belief Functions and Their Application in Data Fusion |
| title_fullStr | A New Correlation Measure for Belief Functions and Their Application in Data Fusion |
| title_full_unstemmed | A New Correlation Measure for Belief Functions and Their Application in Data Fusion |
| title_short | A New Correlation Measure for Belief Functions and Their Application in Data Fusion |
| title_sort | new correlation measure for belief functions and their application in data fusion |
| topic | Dempster–Shafer theory belief correlation measure uncertainty information fusion multi-source data |
| url | https://www.mdpi.com/1099-4300/25/6/925 |
| work_keys_str_mv | AT zhuozhang anewcorrelationmeasureforbelieffunctionsandtheirapplicationindatafusion AT hongfeiwang anewcorrelationmeasureforbelieffunctionsandtheirapplicationindatafusion AT jiantingzhang anewcorrelationmeasureforbelieffunctionsandtheirapplicationindatafusion AT wenjiang anewcorrelationmeasureforbelieffunctionsandtheirapplicationindatafusion AT zhuozhang newcorrelationmeasureforbelieffunctionsandtheirapplicationindatafusion AT hongfeiwang newcorrelationmeasureforbelieffunctionsandtheirapplicationindatafusion AT jiantingzhang newcorrelationmeasureforbelieffunctionsandtheirapplicationindatafusion AT wenjiang newcorrelationmeasureforbelieffunctionsandtheirapplicationindatafusion |