Some novel distance and similarity measures for probabilistic dual hesitant fuzzy sets and their applications to MAGDM

Probabilistic dual hesitant fuzzy set is a more powerful and important tool to express uncertain information. As we all know, the distance and similarity measures are very useful tool in decision-making field. In this study, the distance measure and similarity measure of probabilistic dual hesitation fuzzy set are systematically proposed from the perspectives of discrete and continuous, ordered and unordered, which provides a theoretical support for the research of decision-making problems in probabilistic dual hesitation fuzzy environment. Firstly, we proposed some novel distance and similarity degrees for two probabilistic dual hesitant fuzzy sets and their weighted forms. Secondly, we proposed a decision technique based on the novel built weighted distance and similarity measures to solve the multi-attribute group decision-making problem in the PDHF environment. Finally, the proposed technique was applied to the suitability evaluation of new urbanization. Meanwhile, the technique built in this study was compared with the existed methods to verify the practicability and feasibility, and the superiorities of the built in this study were put forward, which has a better effect in solving multi-attribute group decision-making problems.