Open image in new window Fig. 2 Profit efficiency ranking interval of 14 hospitals.
To illustrate this point, ranking interval for hospital 8 is calculated to be [1, 11].
Based on preference-based index for ranking interval numbers, we define the concept of the preference level as follows.
In interval mathematics, an order relation is often used to rank interval numbers and it implies that an interval number is better than another but not that one is larger than another.
For this purpose, we apply preference-based index for ranking interval numbers introduced by Ruan et al. [28] to treat the interval objective function in the upper level of problem (5).
Similar methodology may be utilized to illustrate ranking intervals of DMUs, or to determine the best and worst profit efficiency rankings of DMUs in Variable Return to Scale, VRS technology.
Ranking intervals in profit efficiency evaluation of observed units may be obtained by utilization of the following Theorems 1 and 2: Optimal objective value in Model 6 is the best profit ranking of DMU k.
We use a preference matrix to determine extremum and rank interval numbers.
A geometric-mean-based possibility degree formula is designed to compare and rank normalized interval multiplicative weights.
