Credit lenders utilize credit rating approaches to provide a classification system for characterizing credit borrowers. In order to measure the borrowers' credibility, that is, ability and willingness to repay the debt, there are many financial and non-financial criteria that should be considered. The basic aim of this study is to propose a multiple-criteria credit rating approach that integrates different kinds of information and represents the borrowers' credibility as a distribution among all the credit ratings. The cumulative belief degree approach is proposed for this purpose. Since all the available information is used in the final representation, a distribution-based credit rating approach is expected to strengthen the lender's inference competency. In order to eliminate subjectivity in the weighting of criteria, an ordered weighted averaging operator is used. Additionally, the credit rating distribution can be transformed into a single credit rating by considering a threshold value. This study proposes a goodness-of-fit test to handle the subjectivity and difficulty of setting the threshold value. The applicability of the proposed approach is demonstrated by analyzing the credibility of selected Turkish firms from the stock exchange market of Turkey. (C) 2017 Wiley Periodicals, Inc.