On approaching full fuzzy data envelopment analysis and its validation

Abstract

We approach the full fuzzy data envelopment analysis (DEA) strictly relying on the extension principle. So far in the literature, fuzzy DEA (that uses fuzzy inputs and outputs but crisp weights) and full fuzzy DEA (that uses fuzzy inputs, outputs and weights) were treated distinctly. However, the crisp weights from fuzzy models only act as crisp weights within optimization, but in fact their feasible values finally describe fuzzy weights. As a consequence, the distinction between full fuzzy models and fuzzy models is due to the distinction between establishing or not an a priori shape for the fuzzy weights. In this paper we advance the idea that the methodologies introduced for fuzzy DEA are valuable for full fuzzy DEA as well; and propose a Monte Carlo simulation algorithm to offer an empirical visualization of the shapes of the fuzzy efficiencies of DMUs in full fuzzy DEA. Such visualization firstly can certify whether a solution approach to a full fuzzy DEA derives solutions complying to the extension principle or not; and secondly discloses the fuzzy shapes of the weights obtained by applying a methodology from fuzzy DEA to solving full fuzzy DEA. The complexity of the proposed algorithm is the same as the solution approach to the crisp DEA model that corresponds to the observed full fuzzy DEA model. We report the numerical results of our experiments, compare them to results found in the recent literature, and discuss the misleading consequences of ignoring the extension principle in the context of full fuzzy DEA. Keywords: data envelopment analysis, efficiency, fuzzy programming.