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.