We use a preference matrix to determine extremum and rank interval numbers.
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.
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.
Models providing ranking intervals for all systems and not only efficient ones.
Salo and Punkka [19] method may now be extended to present the following models for determining profit efficiency ranking intervals.
Individual columns in Fig. 2 refer to the 14 hospital units under study and indicate their individual profit efficiency ranking intervals.
It is recommended that further research concerning ranking intervals of DMUs be conducted based on profit efficiency with price uncertainty to address more practical situations.
The profit efficiency-based ranking intervals presented in this research would help decision makers to acquire information on their system ranking in comparison to other systems.
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.
A more recent ranking technique was introduced by Salo and Punkka [19], which considers all feasible weights and evaluates efficiency dominance relationships for each pair of DMUs by introducing ranking intervals.
