Perturbation Analysis of Evidential Reasoning Rule

Evidential reasoning (ER) rule has been widely used in addressing uncertainty, ignorance, and vagueness information. To explore its performance measure (PM), the perturbation analysis (PA) for the ER rule (ER rule-PA) is conducted, with perturbation taken into consideration. This article aims to analyze the robustness and stability of the ER rule, serving as theoretical basis and technical support for applied research and applications. The combination of two pieces of independent evidence is discussed, and perturbation is added to one piece of evidence. To represent the expected utility of evidence combination under perturbation, perturbation utility is introduced. The novel concept of perturbation coefficient is proposed to characterize the PM of the ER rule (ER rule-PM). The properties of perturbation coefficient are explored to demonstrate the impact of perturbation. The maximum permissible error (MPE) of perturbation coefficient is defined to characterize the acceptability of perturbation. A numerical study is examined to illustrate the implementation process of ER rule-PA. Moreover, a case study of reliability evaluation of aerospace relay is conducted to show the potential applications of ER rule-PA, which makes the proposed method more practical.

[1]  Thierry Denoeux,et al.  Handling possibilistic labels in pattern classification using evidential reasoning , 2001, Fuzzy Sets Syst..

[2]  Jian-Bo Yang,et al.  On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty , 2002, IEEE Trans. Syst. Man Cybern. Part A.

[3]  Dong-Ling Xu,et al.  Evidential reasoning rule for evidence combination , 2013, Artif. Intell..

[4]  Jean Dezert,et al.  Proportional Conflict Redistribution Rule , 2004, ArXiv.

[5]  Yi Yang,et al.  Evaluations of evidence combination rules in terms of statistical sensitivity and divergence , 2014, 17th International Conference on Information Fusion (FUSION).

[6]  Ying-Ming Wang,et al.  A comparison of neural network, evidential reasoning and multiple regression analysis in modelling bridge risks , 2007, Expert Syst. Appl..

[7]  R. Yager.  On the dempster-shafer framework and new combination rules , 1987, Inf. Sci..

[8]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[9]  Fuyuan Xiao,et al.  Multi-sensor data fusion based on the belief divergence measure of evidences and the belief entropy , 2019, Inf. Fusion.

[10]  Chang-Hua Hu,et al.  A New BRB-ER-Based Model for Assessing the Lives of Products Using Both Failure Data and Expert Knowledge , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

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

[12]  Zhi-Jie Zhou,et al.  A New Belief Rule Base Model With Attribute Reliability , 2019, IEEE Transactions on Fuzzy Systems.

[13]  Yong Deng,et al.  Generalized Ordered Propositions Fusion Based on Belief Entropy , 2018, Int. J. Comput. Commun. Control.

[14]  Tetsuya Murai,et al.  Multiple-attribute decision making under uncertainty: the evidential reasoning approach revisited , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[15]  Songtao Xue,et al.  Adaptive sub-interval perturbation-based computational strategy for epistemic uncertainty in structural dynamics with evidence theory , 2018, Probabilistic Engineering Mechanics.

[16]  Christos G. Cassandras,et al.  A new approach to the analysis of discrete event dynamic systems , 1983, Autom..

[17]  Yong Deng,et al.  Evaluation method based on fuzzy relations between Dempster–Shafer belief structure , 2018, Int. J. Intell. Syst..

[18]  M. Singh,et al.  An Evidential Reasoning Approach for Multiple-Attribute Decision Making with Uncertainty , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[19]  Yu-chi Ho,et al.  A gradient technique for general buffer storage design in a production line , 1979, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[20]  Chang-Hua Hu,et al.  A Model for Hidden Behavior Prediction of Complex Systems Based on Belief Rule Base and Power Set , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[21]  Jian-Bo Yang,et al.  The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties , 2006, Eur. J. Oper. Res..

[22]  Jian-Bo Yang,et al.  A data-driven approximate causal inference model using the evidential reasoning rule , 2015, Knowl. Based Syst..

[23]  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.

[24]  Jian-Bo Yang,et al.  Belief rule-base inference methodology using the evidential reasoning Approach-RIMER , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[25]  Jian-Bo Yang,et al.  Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties , 2001, Eur. J. Oper. Res..

[26]  Jian-Bo Yang,et al.  A General Multi-Level Evaluation Process for Hybrid MADM With Uncertainty , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[27]  Éloi Bossé,et al.  Robust combination rules for evidence theory , 2009, Inf. Fusion.

[28]  Xi-Ren Cao,et al.  Perturbation analysis of discrete event dynamic systems , 1991 .

[29]  R. Haenni.  Shedding new light on Zadeh's criticism of Dempster's rule of combination , 2005, 2005 7th International Conference on Information Fusion.

[30]  D-S证据理论的 Ctect.  An experimental method of CT / ECT image fusion based on DS evidence theory , 2018 .