An effective method for evaluating the efficiency of peer decision-making units (DMUs) is data envelope analysis (DEA). In engineering sciences and real-world management problems, uncertainty in input and output data always exists. To achieve reliable results, uncertainties must be taken into account. In this research, a General Fuzzy (GF) approach is designed to cope with uncertainty in the presence of fuzzy observations for categorizing and specifying stability radius and alterations ranges of efficient and inefficient DMUs, which is applicable to real-world decision-making problems. For this purpose, a DEA sensitivity analysis model is presented, which will be modeled by fuzzy sets. Then, by applying the General Fuzzy (GF) approach, the fuzzy DEA sensitivity analysis model is transformed into the equivalent crisp form of fuzzy chance constraints according to specific confidence levels. Finally, a numerical example and a case study of branches of the social security organization are presented to illustrate sensitivity and stability analysis in the presence of fuzzy data. The obtained results provide the input and output changes of the evaluated units according to the attitude and preference of the decision maker with different confidence levels so that the data changes in the fuzzy environment do not change the units' classification from efficient to inefficient and vice versa.