Applying Convex Hesitant Fuzzy Sets in Decision-Making Problems

P. Huidobro Fernández, P. Alonso Velázquez, V. Janis, S. Montes Rodríguez

Fuzzy sets, proposed by Zadeh in 1965, handle imprecision using membership degrees (0 to 1). Hesitant fuzzy sets extend classical fuzzy tools for greater efficiency and diverse applications. We focus on typical hesitant fuzzy sets with finite membership values.

Convexity of fuzzy sets and extensions has been studied since Zadeh's work.

Decision-making involves alternatives, limitations, and a utility function. Fuzzy sets help handle imprecision in defining objectives and limitations.

We define convex hesitant fuzzy sets based on orders. When using admissible orders, orders refining the lattice order, our convexity aligns with level sets, making them convex crisp sets. We also define intersection of hesitant fuzzy sets, recovering classical interpretation. With this intersection and convexity, we achieve good results in optimization and apply them in decision-making with convex hesitant fuzzy goals and constraints.

Keywords: Hesitant fuzzy sets, convexity, decision-making

Operations Research Methods and Applications
November 9, 2023  3:30 PM
HC1: Canónigos Room 1

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