GRP and CRITIC method for probabilistic uncertain linguistic MAGDM and its application to site selection of hospital constructions

The probabilistic uncertain linguistic term sets could depict uncertain information well and the grey relational projection (GRP) method is appropriate to rank various alternatives. In such paper, we develop a GRP method for probabilistic uncertain linguistic MAGDM (PUL-MAGDM) based on the criteria importance through intercriteria correlation (CRITIC) method. The attribute weights are determined by CRITIC method. Furthermore, the probabilistic uncertain linguistic positive ideal solution (PULPIS) and probabilistic uncertain linguistic negative ideal solution (PULNIS) are introduced. Then, the optimal scheme is obtained through figuring up the value of grey relational projection (GRP) from probabilistic uncertain linguistic positive ideal solution (PULPIS) as well as probabilistic uncertain linguistic negative ideal solution (PULNIS). At last, to verify the validity of the extended method, a numerical example to further account for site selection of hospital constructions is put into use. The result manifests that the proposed method is effective. It is feasible to utilize the method to handle selecting problems in other areas.