In this article, we investigate the measurement of performance in DMUs in which input and/or output values are given as imprecise data. By imprecise data, we mean that in some cases, we only know that the actual values are inside certain intervals, and in other cases, data are specified only as ordinal preference information. In this article, we present two distinct perspectives for determining the upper and lower bounds of the efficiency the DMU under evaluation can have with imprecise data: (1) The optimistic perspective, which uses DEA-efficient production frontier, and seeks the best score among various values of the efficiency score; the measured efficiency in this perspective is called the best relative efficiency or the optimistic efficiency. (2) The pessimistic perspective, which uses inefficiency frontier, also called input frontier, and seeks the lowest score among various values of the efficiency score; the measured efficiency in this perspective is called the worst relative efficiency or the pessimistic efficiency. For this reason and contrary to some DEA-related studies, we do not restrict our attention only to precise data. We will investigate a more general case of dealing with imprecise data, providing a method for obtaining the upper and lower bounds of efficiency. Two numerical examples will be presented to illustrate the application of the proposed DEA approach.‎‎ Manuscript profile

Data envelopment analysis (DEA) has been proven as an efficient technique to evaluate the performance of homogeneous decision making units (DMUs) where multiple inputs and outputs exist. In the conventional applications of DEA, the data are considered as specific numerical values with explicit designation of being an input or output. However, the observed values of the data are sometimes imprecise (i.e. input and output variables cannot be measured precisely) and data are sometimes flexible (measures with unknown status of being input or output are referred to as flexible measures in the literature). In the current paper a number of methods are proposed to evaluate the relative efficiency and to identify the status of fuzzy flexible measures. Indeed, the modified fuzzy DEA models are suggested to accommodate flexible measures. In order to obtain correct results, alternative optimal solutions are considered to deal with the fuzzy flexible measures. Numerical examples are used to illustrate the ‎procedure.‎ Manuscript profile