A new belief rule base inference methodology with interval information based on the interval evidential reasoning algorithm

Focusing on the problem that current belief rule-based system cannot effectively deal with interval uncertainty, this paper investigates the belief rule-based system under overall interval uncertainty, where interval data, interval belief degree, and grade interval are considered simultaneously, and the interval belief rule-based system (IBRBS) is proposed based on the analysis. Firstly, the interval belief rule base (IBRB) was established with interval belief distributions embedded in both the antecedent and consequent terms of each rule, which is capable of capturing interval uncertainty and incompleteness in an integrated way. Then, the activation weight calculation method using the nonlinear optimization model is proposed, and the analytical interval evidential reasoning (IER) algorithm is applied as the inference method to combine activated rules under interval uncertainty. Finally, two case studies are presented to illustrate the effectiveness of the proposed method. Results show that the proposed method can be regarded as the generalized form of belief rule-based system, and could effectively deal with interval uncertainty.