Measuring Transport Systems Efficiency under Uncertainty by Fuzzy Sets Theory based Data Envelopment Analysis

A crucial step in transportation planning process is the measure of systems efficiency. Many efforts have been made in this field in order to provide satisfactory answer to this problem. One of the most used methodologies is the Data Envelopment Analysis (DEA) that has been applied to a wide number of different situations where efficiency comparisons are required. The DEA technique is a useful tool since the approach is non-parametric, and can handle many output and input at the same time. In a lot of real applications, input and output data cannot be precisely measured. Imprecision (or approximation) may be originated from indirect measurements, model estimation, subjective interpretation, and expert judgment of available information. Therefore, methodologies that allow the analyst to explicitly deal with imprecise or approximate data are of great interest, especially in freight transport where available data as well as stakeholders’ behavior often suffer from vagueness or ambiguity. This is particularly worrying when assessing efficiency with frontier-type models, such as Data Envelopment Analysis (DEA) models, since they are very sensitive to possible imprecision in the data set. The specification of the evaluation problem in the framework of the fuzzy set theory allows the analyst to extend the capability of the traditional “crisp” DEA to take into account and, thus, to represent the uncertainty embedded in real life problems. The existing fuzzy approaches are usually categorized in four categories: a) the tolerance approaches; b) the defuzzification approaches c) the α- level based approaches; d) the fuzzy ranking. In this paper, we have explored the Fuzzy Theory-based DEA model, to assess efficiency measurement for transportation systems considering uncertainty in data, as well as in the evaluation result. In particular, the method is then applied to the evaluation of efficiency of container ports on the Mediterranean See with a sensitivity analysis in order to investigate the properties of the different approaches. The results are then compared with traditional DEA.