Data envelopment analysis (DEA) has been genuinely known as an impeccable technique for efficiency measurement. In practice, since many production systems such as broadcasting companies, banking institutions and R&D organisations include two processes connected in series, we have need of utilising two-stage DEA models to identify the sources of inefficiency and explore in turn appropriate options for improving performance. The lack of the ability to generate the actual weights is not only an ongoing challenge in traditional DEA models, it can also have serious repercussion for the contemporary DEA models (e.g., two-stage DEA). This paper presents a common-weights method for two-stage structures that allows us to consider equality of opportunity in a fuzzy environment when evaluating the system efficiency and the component process efficiencies. The proposed approach first seeks upper bounds on factor weights and then determines a set of common weights by a single linear programming problem. We illustrate the developed approach with a data set taken from the literature.