Finding a Common Set of Weights in Fuzzy DEA

Data Envelopment Analysis (DEA) is a mathematical programming approach for assessing relative efficiencies within a group of Decision Making Units (DMUs). An important outcome of such an analysis is a set of virtual multipliers or weights accorded to each (input or output) factor taken into account. These sets of weights are, typically, different for each of the participating DMUs, and in some cases it may be considered unacceptable that the same factor is accorded widely differing weights. Thus, it is important to find a Common Set of Weights (CSW) across the set of DMUs. In this paper, a procedure is suggested to find a CSW in fuzzy DEA. In this procedure, by assessing upper bounds on factor weights, the weight flexibility is restricted. Then, a CSW is determined by compacting these intervals. Since resulted efficiencies by the proposed CSW are fuzzy numbers rather than crisp values, it is more useful for decision maker. To demonstrate the concept, a numerical example is solved.

Keywords:

Data Envelopment Analysis , Common Set of Weights , Fuzzy Number , Membership Function