Data envelopment analysis (DEA) is an approach to measuring the relative efficiency of a set of decision making units (DMUs) with multiple inputs and multiple outputs using mathematical programming. The traditional DEA, which is based: on the concept of efficiency frontier (output frontier), determines the, best efficiency score that can be assigned to each DMD. Based on these-scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA non-efficient (optimistic non-efficient) units, and the DEA-efficioot DMUs determine the efficiency frontier. There is a comparable approach, which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient: or pessimistic inefficient, and those DMUs that do not lie on the inefficient froatier are declared to be DEA-non-inefficient or pessimistic non-inefficient. In-this paper, we argue that both relative efficiencies should be considered' simultaneously, and any approach that considers only one of them will tie biased. For measuring the overall performance of the DMUs, we propose. to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models, In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numeric example about Iranian gas companies will be evaluated using the DEA approach' with efficient and inefficient frontiers to show its convenience and-usefulness.