Probability-Based Integration for Continuous Hesitant Fuzzy Information in Group Decision-Making

This section initially combines the probability theory to introduce the concept of continuous hesitant fuzzy element (CHFE). Following this, the concept of uniform hesitant fuzzy element (UHFE) is proposed, and discrete (probabilistic) hesitant fuzzy information is transferred to continuous one, benefitted from the connection between UHFEs and CHFEs with uniform distribution. Subsequently, integration methods of CHFEs based on mathematical derivation are developed, which lays a theoretical foundation for the continuity of hesitant fuzzy information. Additionally, a simpler aggregation method of CHFEs based on computer simulation is introduced to simplify and enhance the effectiveness of CHFEs when applied to solve decision-making problems. Finally, an example of evaluating water resources emergency management plans is provided to demonstrate the application of the aforementioned methods in practical decision-making problems.