Establishing the existence of a distance-based upper bound for a fuzzy DEA model using duality

In a recent paper [Soleimani-damaneh M. Fuzzy upper bounds and their applications. Chaos, Solitons & Fractals 2008;36:217–25.], I established the existence of a distance-based fuzzy upper bound for the objective function of a fuzzy DEA model, using the properties of a discussed signed distance, and provided an effective approach to solve that model. In this paper a new dual-based proof for the existence of the above-mentioned upper bound is provided which gives a useful insight into the theory of fuzzy DEA.