A multi-granularity proportional hesitant fuzzy linguistic TODIM method and its application to emergency decision making

Proportional hesitant fuzzy linguistic sets (PHFLSs), is a good way of representing uncertain assessment of decision makers. This paper focuses on extending the Interactive and Multiple Attribute Decision Making (TODIM) method into multi-granularity PHFLSs environment. We first propose a new ranking method and a normalized Hamming distance measure of multi-granularity PHFLSs, which can be used to measure and compare multi-granularity PHFLSs and is associated with lower computational complexity. Next, we develop the multi-granularity proportional hesitant linguistic TODIM approach, where the criteria weights are derived by using incomplete weight information. Finally, a case study on mine emergency decision making problem is presented to demonstrate the effectiveness of the proposed method.