A Linear Programming Method Based on Probabilistic Linguistic Kolmogorov-Smirnov Distance for Hospital Service Quality Evaluation

Distance measures are important in the framework of multi-criterion decision making with probabilistic linguistic term sets. However, few studies investigated the distance of probabilistic linguistic term sets from the perspective of probability distributions. Due to this fact, this paper originally proposes a probabilistic linguistic Kolmogorov-Smirnov distance measure to identify the gaps between probability distributions. As a basis of this distance measure, the cumulative probability distributions of probabilistic linguistic term sets are introduced. Then, a common basic scale is given to get the probabilistic linguistic Kolmogorov-Smirnov distance between the probabilistic linguistic term sets with different lengths. After that, a linear programming technique for multidimensional analysis of preferences is developed based on the probabilistic linguistic Kolmogorov-Smirnov distance. An illustration of the hospital service quality evaluation is solved by the proposed method, and a sensitivity analysis is done to demonstrate the reliability of the results.