Nuclear safeguards evaluation (NSE) is to verify that a State is living up to its international undertakings not to use nuclear programs for nuclear weapons purposes. The main issue in NSE is on the aggregation of expert evaluations for numerous indicators to make a final decision about the State's nuclear activity. Fuzzy multiple attribute decision making (FMADM) methods are capable of dealing with such an issue. In this study, we propose a new FMADM methodology to solve the NSE problem. To this end, we investigate the applicability of four basic FMADM methods, namely a simple additive weighting method, a TOPSIS method, a linguistic method, and a non-compensatory method, to the NSE issue. As a result of the assessment of the basic methods, we propose a new FMADM methodology based on a new aggregation operator in which a cumulative belief structure is used to represent the expert evaluations. The basic methods and the proposed method as well are applied to an example from the literature for illustration purposes.