Environmental quality evaluation based on the TODIM method with normal wiggly hesitant fuzzy set

The normal wiggly hesitant fuzzy set (NWHFS) is one of the latest extensions of hesitant fuzzy set (HFS). It can depict experts' preference information consisting of several possible values and the potential information dug in the traditional hesitant fuzzy set (HFS) at the same time. However, traditional aggregation operators of NWHFSs always ignore the influence of psychological behaviors. Therefore, to make use of the potential information and manage the applications with incomplete rationality, this paper combines the advantages of TODIM (TOmada deDecisao Iterativa Multicriterio) method and NWHFSs. Considering the structures and characteristics of NWHFSs, we also provide the definition of distance measure of NWHFSs. Based on this, we develop an improved TODIM method. The specific implementation process is also provided. Finally, we apply the improved TODIM method to the environmental quality evaluation. The comparison result with traditional aggregation operators indicates that the proposed method can enlarge the competitive relationship better. It also demonstrates the rationality and accuracy of our method.