Research on Probabilistic Language Multi-Attribute Group Decision-Making Method Based on Correlation Coefficient and Improved Entropy

To address the issue of unknown expert and attribute weights in the comprehensive assessment of hospitals, as well as the potential challenges posed by distance measures, this paper presents a probabilistic language multi-attribute group decision-making (MAGDM) approach that utilizes correlation coefficients and improved entropy. First, the correlation function, called the probabilistic linguistic correlation coefficient, is introduced into the probabilistic linguistic term set(PLTS) to measure the consistency among experts, so as to obtain the weights of experts. Next, based on Shannon entropy, an improved probabilistic linguistic entropy is proposed to measure the uncertainty of PLTS considering the number of alternatives and information quantity. Then, based on the correlation coefficient and improved entropy, the attribute weights are obtained. In addition, in order to overcome the counter-intuitive problem of existing distance measurement, this paper proposes a probabilistic language distance measurement method based on the Bray-Curtis distance to measure the differences between PLTSs. On this basis, by applying the technique for order preference by similarity to ideal solution (TOPSIS) method and using PLTSs to construct the MAGDM method, the ranking of alternative schemes is generated. Finally, the improved MAGDM method is applied to an example of the comprehensive evaluation of the smart medical hospitals. The results show that compared with the existing methods, this method can determine the weight information more reasonably, and the decision-making results are not counter-intuitive, so it can evaluate the hospital more objectively.