A new correlation coefficient of BPA based on generalized information quality

Dempster rule is commonly used to combine evidence from different sensors because of its excellent mathematical properties (commutativity and associativity). However, the conflict coefficient k of this rule cannot be reasonably and effectively express the conflict between evidence, which makes the Dempster rule greatly questioned. To describe in the relationship between evidence (conflict or correlation) more accurately, an evidence correlation coefficient based on generalized information quality is proposed. First of all, according to Deng entropy to measure the uncertainty of each evidence, and combined with the information quality of Yager, new generalized information quality is proposed, which performs well in measuring the basic probability assignment's certainty. Second, the evidence itself is modified by generalized information quality, and the evidence correlation coefficient is calculated based on the Pearson coefficient formula. A new measurement method of evidence conflict based on evidence correlation coefficient is proposed. Finally, combined with the evidence correlation coefficient and DEMATEL model, the evidence is discounted and combined. Numerous examples are used to analyze and compare the evidence conflict coefficient and the evidence combination results. The experimental results demonstrate that, compared with other evidence conflict measurement methods, the evidence conflict coefficient calculated by this method can reflect the difference between evidence more effectively. The result of evidence combination is more reasonable and accurate.

[1]  Lei Chen,et al.  A New Method to Handle Conflict when Combining Evidences Using Entropy Function and Evidence Angle with an Effective Application in Fault Diagnosis , 2020 .

[2]  Yongchuan Tang,et al.  An Extended Base Belief Function in Dempster–Shafer Evidence Theory and Its Application in Conflict Data Fusion , 2020, Mathematics.

[3]  Yongchuan Tang,et al.  A New Fuzzy-Evidential Controller for Stabilization of the Planar Inverted Pendulum System , 2016, PloS one.

[4]  Yong Wang,et al.  An evidence combination approach based on fuzzy discounting , 2020, Soft Computing.

[5]  Huchang Liao,et al.  Generalised probabilistic linguistic evidential reasoning approach for multi-criteria decision-making under uncertainty , 2019, J. Oper. Res. Soc..

[6]  Yong Deng,et al.  Generalized Belief Entropy and Its Application in Identifying Conflict Evidence , 2019, IEEE Access.

[7]  Zeshui Xu,et al.  A survey of decision-making methods with probabilistic linguistic information: bibliometrics, preliminaries, methodologies, applications and future directions , 2020, Fuzzy Optim. Decis. Mak..

[8]  Jiexin Pu,et al.  A Weighted Evidence Combination Method Based on the Pignistic Probability Distance and Deng Entropy , 2020 .

[9]  Liang Zhao,et al.  A novel Dempster-Shafer theory-based approach with weighted average for failure mode and effects analysis under uncertainty , 2020 .

[10]  Henri Prade,et al.  Representation and combination of uncertainty with belief functions and possibility measures , 1988, Comput. Intell..

[11]  Fuyuan Xiao,et al.  A method for combining conflicting evidences with improved distance function and Tsallis entropy , 2020, Int. J. Intell. Syst..

[12]  Yong Deng.  Information Volume of Mass Function , 2020, Int. J. Comput. Commun. Control.

[13]  Malcolm James Beynon,et al.  The Role of the DS/AHP in Identifying Inter-Group Alliances and Majority Rule Within Group Decision Making , 2006 .

[14]  Jixiang Deng,et al.  Information Volume of Fuzzy Membership Function , 2021, Int. J. Comput. Commun. Control.

[15]  Ji-yao An,et al.  Combination of Evidence with Different Weighting Factors: A Novel Probabilistic-Based Dissimilarity Measure Approach , 2015, J. Sensors.

[16]  Yuan Jiang,et al.  Multisensor Decision Approach for HVCB Fault Detection Based on the Vibration Information , 2021, IEEE Sensors Journal.

[17]  Francisco Herrera,et al.  Group decision making with double hierarchy hesitant fuzzy linguistic preference relations: Consistency based measures, index and repairing algorithms and decision model , 2019, Inf. Sci..

[18]  Lotfi A. Zadeh,et al.  On the Validity of Dempster''s Rule of Combination of Evidence , 1979 .

[20]  Yafei Song,et al.  Evidence combination based on credibility and separability , 2014, 2014 12th International Conference on Signal Processing (ICSP).

[21]  Hanping Zhao,et al.  Rapid assessment of building collapse based on sequential dynamic fusion of multi-source disaster information from news media , 2020 .

[22]  Florentin Smarandache,et al.  Advances and Applications of Dezert-Smarandache Theory (DSmT) for Information Fusion (Collected works), Vol. 2 , 2006 .

[23]  Jiao-Jiao Zhong,et al.  Generalized combination rule for evidential reasoning approach and Dempster-Shafer theory of evidence , 2021, Inf. Sci..

[24]  Zied Elouedi,et al.  How to preserve the conflict as an alarm in the combination of belief functions? , 2013, Decis. Support Syst..

[25]  Fabio Cuzzolin.  Belief functions: Theory and applications (BELIEF 2014) , 2016, Int. J. Approx. Reason..

[26]  S. Si,et al.  DEMATEL Technique: A Systematic Review of the State-of-the-Art Literature on Methodologies and Applications , 2018 .

[27]  Ronald R. Yager,et al.  An intelligent quality-based approach to fusing multi-source probabilistic information , 2016, Inf. Fusion.

[28]  Quan Pan,et al.  Combination of Classifiers With Optimal Weight Based on Evidential Reasoning , 2018, IEEE Transactions on Fuzzy Systems.

[29]  Fuyuan Xiao,et al.  A Novel Conflict Measurement in Decision-Making and Its Application in Fault Diagnosis , 2020, IEEE Transactions on Fuzzy Systems.

[30]  Yong Deng,et al.  Combination of Evidential Sensor Reports with Distance Function and Belief Entropy in Fault Diagnosis , 2019, Int. J. Comput. Commun. Control.

[31]  R. Yager.  Hedging in the Combination of Evidence , 1983 .

[32]  Chunhe Xie,et al.  A modified method for risk evaluation in failure modes and effects analysis of aircraft turbine rotor blades , 2016 .

[33]  N. A. Rahman,et al.  A Course in Theoretical Statistics , 1970 .

[34]  Wen Jiang,et al.  An evidential sensor fusion method in fault diagnosis , 2016 .

[35]  M. Beynon,et al.  The Dempster-Shafer theory of evidence: an alternative approach to multicriteria decision modelling , 2000 .

[36]  Yong Deng,et al.  Dependent Evidence Combination Based on Shearman Coefficient and Pearson Coefficient , 2018, IEEE Access.

[37]  Yu Liu,et al.  Evidence Combination Based on Credal Belief Redistribution for Pattern Classification , 2020, IEEE Transactions on Fuzzy Systems.

[38]  Florentin Smarandache,et al.  Advances and Applications of DSmT for Information Fusion (Collected Works) , 2004 .

[39]  R. W. Blackmor,et al.  A Course in Theoretical Statistics , 1970 .

[40]  Peng Huang,et al.  Soft measurement of ball mill load based on multi-classifier ensemble modelling and multi-sensor fusion with improved evidence combination , 2020, Measurement Science and Technology.

[41]  Philippe Smets,et al.  The Combination of Evidence in the Transferable Belief Model , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[42]  Éloi Bossé,et al.  A new distance between two bodies of evidence , 2001, Inf. Fusion.

[43]  Florentin Smarandache,et al.  Advances and Applications of DSmT for Information Fusion , 2004 .

[44]  Fuyuan Xiao,et al.  Aggregation of uncertainty data based on ordered weighting aggregation and generalized information quality , 2019, Int. J. Intell. Syst..

[45]  Florin Gheorghe Filip,et al.  Fuzzy Logic Is Not Fuzzy: World-renowned Computer Scientist Lotfi A. Zadeh , 2017, Int. J. Comput. Commun. Control.

[46]  A. Gabus,et al.  World Problems, An Invitation to Further Thought within the Framework of DEMATEL , 1972 .

[47]  Lipeng Pan,et al.  Probability Transform Based on the Ordered Weighted Averaging and Entropy Difference , 2020, Int. J. Comput. Commun. Control.

[48]  Xingjian Wang,et al.  A Novel Conflicting Evidence Discounting Method Based on TOPSIS Decision-Making , 2018, 2018 IEEE CSAA Guidance, Navigation and Control Conference (CGNCC).

[49]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[50]  Kang Hao Cheong,et al.  Multisource basic probability assignment fusion based on information quality , 2021, Int. J. Intell. Syst..

[51]  Catherine K. Murphy.  Combining belief functions when evidence conflicts , 2000, Decis. Support Syst..

[52]  András Czmerk,et al.  Algorithmic Enhancement of Automotive MEMS Gyroscopes With Consumer-Type Redundancy , 2021, IEEE Sensors Journal.

[53]  Wen Jiang,et al.  A correlation coefficient of belief functions , 2016, Int. J. Approx. Reason..

[54]  Qi Liu,et al.  Combining belief functions based on distance of evidence , 2004, Decis. Support Syst..

[55]  Yong DENG,et al.  Uncertainty measure in evidence theory , 2020, Science China Information Sciences.

[56]  Eric Lefevre,et al.  Belief function combination and conflict management , 2002, Inf. Fusion.

[57]  Peter Walley,et al.  Measures of Uncertainty in Expert Systems , 1996, Artif. Intell..