Several similarity measures of probabilistic dual hesitant fuzzy sets and their applications to new energy vehicle charging station location

Abstract

Probabilistic dual hesitant fuzzy set (PDHFS) can better reflect the hesitant attitude and probability information of decision-makers than existing fuzzy sets. Therefore, it is a more powerful and important tool to express and deal with uncertain information. The score function of fuzzy number plays a very important role in comparing two fuzzy numbers. Entropy measure is a very effective tool for weighting decision attributes in multi-attribute group decision-making problems. Firstly, depending on the detailed analysis of the already existed score function of probabilistic dual hesitant fuzzy element (PDHFE), we built a novel score function for it, it is more effective and convenient when comparing two elements. Secondly, probabilistic dual hesitant fuzzy entropy was built to weight decision attributes. Thirdly, a combined weighting method was proposed which can reflect both subjective and objective information for decision attribute weighting based on the principle of minimum discriminant information. Fourthly, we extended the classical Dice and Jaccard similarity measures to the probabilistic dual hesitant fuzzy environment, and an all-new multi-attribute group decision-making technique to solve the problem that the decision attribute information is probabilistic dual hesitant fuzzy element. Finally, the applicability and effectiveness of this technique are proved by numerical examples and comparative analysis.

Keywords

• Score function
• Entropy measure
• Dice similarity measure
• Jaccard similarity measure
• Multi-attribute group decision-making
• Probabilistic dual hesitant fuzzy set