Convexity of typical hesitant fuzzy sets applied to decision-making problems

Abstract Handling uncertainty in decision-making often requires flexible models that can accommodate multiple possible membership degrees. Typical hesitant fuzzy sets provide such a framework but pose challenges in comparison and mathematical consistency. In this work, we introduce a novel definition of convexity for typical hesitant fuzzy sets based on order relations, ensuring that level sets remain convex crisp sets under admissible orders. Additionally, we redefine intersection and union to recover classical fuzzy set properties while maintaining consistency within the hesitant fuzzy framework. Leveraging these notions, we develop a decision-making methodology where constraints and goals are modeled using convex THFS. This approach enhances optimization processes, guaranteeing coherent and globally optimal solutions, making THFS a more powerful tool for decision analysis in uncertain environments.