In this paper, an interval-valued belief rule inference methodology based on evidential reasoning (IRIMER) is proposed, which includes the interval-valued belief rule representation scheme and its inference methodology. This interval-valued belief rule base is designed with interval-valued belief degrees embedded in both the consequents and the antecedents of each rule, which can represent uncertain information or knowledge more flexible and reasonable than the previous belief rule base. Then its inference methodology is developed on the interval-valued evidential reasoning (IER) approach. The IRIMER approach improves and extends the recently uncertainty inference methods from the rule representation scheme and the inference framework. Finally, a case is studied to demonstrate the concrete implementation process of the IRIMER approach, and comparison analysis shows that the IRIMER approach is more flexible and effective than the RIMER [J. B. Yang, J. Liu, J. Wang, H. S. Sii and H. W. Wang, Belief rule-base interference methodology using the evidential reasoning approach-RIMER, IEEE Transaction on Systems Man and Cybernetics Part A-Systems and Humans36 (2006) 266–285.] approach and the ERIMER [J. Liu, L. Martínez, A. Calzada and H. Wang, A novel belief rule base representation, generation and its inference methodology, Knowledge-Based Systems 53 (2013) 129–141.] approach.
An Uncertainty Measure for Interval-valued Evidences