A belief Rule-base Inference Methodology using the Evidential Reasoning approach (RIMER) has been developed recently, which is an extension of traditional rule based systems and is capable of representing more complicated causal relationships using different types of information with uncertainties. A rule-base in RIMER is designed with belief degrees embedded in all possible consequents of a rule, where it is assumed that all the consequents are independent of each other in order to accommodate the assumption imposed on the evidential reasoning (ER) algorithm being used. To overcome this limitation, in the paper, we extend the RIMER approach to the case of fuzzy consequents, that is, each consequent can be defined as a fuzzy linguistic term because of vagueness and inexactness. In such cases, the intersection of adjacent two fuzzy sets is no longer an empty set, which results in the above ER algorithm inapplicable during the inference process, instead, the inference of the belief rule-based system is implemented using an extended fuzzy ER algorithm. This work extends the applicality and feasibility of the RIMER approach.