The fault diagnosis method of signed directed graphs (SDGs) has difficulties verifying the seriousness of an abnormal process variable and providing an accurate resolution of fault origin, when the abnormal variable is in the neighborhood of the designed threshold. In this paper, the fuzzy set theory was incorporated into SDGs to overcome these obstacles. This proposed algorithm begins with an SDG representing the qualitative cause-effect relations among the process variables. The primarily formulated SDG is then simplified by edge consistency and the combination of unmeasured variables, an acyclic graph consisting of strongly connected components was formed, and then the technique of the depth-first search determined the specific strong component where the possible fault origin was located. Finally, the quantitative fuzzy set manipulation was introduced, the degree of membership of the process variables was determined, and then the variables were sequentially arranged by their degree of membership to determine the possible fault origins. A process consisting of a jacketed CSTR and a vaporizer with a designated plugged product valve was diagnosed by the proposed approach. The result shows that the proposed approach improves the accuracy of resolution and provides more valuable information on the arrangement of fault origin candidates by the seriousness of the abnormality of the variables.