New Similarity Measures for Dual Hesitant Fuzzy Sets and Their Application

Dual hesitant fuzzy sets (DHFSs) are powerful and efficient to express hesitant preferred and non-preferred information simultaneously. This paper focuses on similarity measures for DHFSs. To do this, it first analyzes the limitations of previous similarity measures for DHFSs. Then, several new dual hesitant fuzzy similarity measures are defined that can avoid the issues of previous ones. To discriminate the importance of decision-making criteria, several weighted similarity measures are further defined in views of additive and 2-additive measures. When the weighting information is not exactly known, optimization methods for determining additive and 2-additive measures are built, respectively. Furthermore, a method for multi-criteria decision-making based on new weighted similarity measures is developed. Finally, two numerical examples are provided to show the utilization of the new method and compare with previous methods.