Stability of RTS of efficient DMUs in DEA with fuzzy u0 under fuzzy data

An important property of production functions is the concept return to scale (RTS) as found in the literature. There are two common variations RTS in data envelopment analysis (DEA) used, constant return to scale (CRS) and variation return to scale (VRS). The envelopment surface in BCC model is VRS and this is the result of the presence of the convexity constraint in the dual model and, equivalently, the presence of new separate variable, usually called u0, is introduced in the primal model which makes it possible to determine whether operations were led in the areas of constant, increasing and decreasing. In conventional BCC model make an assumption that input-output data and are exact. While accurate measurement in many real applications due to either non-availability of sophisticated measurement tools or qualitative nature of the phenomena may not be possible, consequently, this information can be represented as fuzzy numbers or linguistic terms. In this paper the RTS of efficient decision making units (DMUs) are investigated in BCC model where fuzziness is considered in both inputs and outputs and variable u0. The proposed models provide the stability of fuzzy u0 as interval region, consequently analyst can easily examine the sensitivity of RTS of efficient DMUs. Using alpha-cut, an alternative approach is suggested to solve the obtained model. To illustrate the proposed method, a numerical example is solved.