Fronteiras DEA Difusas

the ``fuzzy'' dea frontier is applied in situations where some variables (inputs or outputs) present a certain degree of uncertainty in its measurement, without any assumption about the probability distribution function. we build the efficient frontier taking in account the minor and major values of the input (or output). the efficient frontier is, in that case, a fuzzy set, to which the dmus have a degree of membership. in order to compute the degree of membership two frontiers are constructed: the optimistic and the pessimistic frontiers. as this indicator isn't an efficiency score, we introduce the inverted frontier concept, which allows the fuzzy-dea efficiency score computation. we developed the case where only one variable present a certain degree of uncertainty and it is generalised to the case where some or all variables are uncertain.