Relationship between efficiency in the traditional data envelopment analysis and possibility sets

•A fuzzy interpretation of the technical efficiency is argued.•We present a new presentation of the DEA model based on fuzzy concept.•We prove that the optimal values of DEA and the proposed model are the same.

In this paper, the relationship between possibility sets, a fuzzy number concept, and efficiency score in Data Envelopment Analysis (DEA) is dealt with. A new DEA model for handling crisp data using fuzzy concept is proposed. The model which is equivalent to a traditional DEA model is then extended to incorporate situations whereby some inputs, in a fuzzy sense, are almost discretionary variables. With this relationship, a new perspective of viewing and exploring other DEA models is now made possible.