Perturbation Analysis of Evidential Reasoning Rule

• Published in: IEEE transactions on systems, man, and cybernetics. Systems Vol. 51; no. 8; pp. 4895 - 4910
• Main Authors: Tang, Shuai-Wen, Zhou, Zhi-Jie, Hu, Chang-Hua, Yang, Jian-Bo, Cao, You
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aerospace relay; Coefficients; Cognition; Decision making; Erbium; Evidential reasoning; evidential reasoning (ER) rule; Expected utility; Permissible error; perturbation analysis (PA); perturbation coefficient; Perturbation methods; perturbation utility; Reliability analysis; Robustness (mathematics); Stability analysis; Technical services; Uncertainty
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2019.2944640

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.