The application of Dempster Shafer theory for combining multiple sources of evidence to handle the uncertainties present in engineering systems is well established. In this work, a fuzzy approach is presented for the safety analysis of uncertain engineering systems in the presence of multiple sources of evidence. The α-cut approach is used to represent the fuzzy membership functions of the uncertain parameters. The existence of large epistemic uncertainty information for each of the uncertain parameters is assumed to be available in the form of interval-valued data from multiple sources. The fuzzy membership function of the response of the system (such as the margin of safety) is computed by applying fuzzy arithmetic to the mathematical formulation of the system. A new procedure is introduced to calculate bounds on the response of the system such as the margin of safety. A new methodology, termed the Weighted Fuzzy Theory for Intervals (WFTI), is proposed for combining evidence when different credibilities are associated with the various sources of evidence. The application of the proposed methods is illustrated by considering the design of a welded beam involving multiple uncertain parameters. The results obtained using the proposed WFTI method are verified to converge to those obtained using the fuzzy approach when all the credibilities tend to have an identical value of unity.