Normalized Hesitant Fuzzy Aggregation Operators for Multiple Attribute Decision-Making

As a powerful tool for depicting uncertain information, hesitant fuzzy elements (HFEs) have been favored by many experts and scholars. Consequently, the aggregation of HFEs plays an imperative role in both theory and practice. Although there exist many kinds of hesitant fuzzy aggregation operators nowadays, limitations and irrationality still exist because they cannot satisfy some basic properties of a valid aggregation operator, such as idempotency and boundedness. Motivated by this case, this article aims to develop some novel hesitant fuzzy aggregation operators for handling HFEs that can satisfy three basic properties of a reliable aggregation operator. We first define two normalized operations on HFEs that avoid crossover operation. Furthermore, we propose some normalized aggregation operators from the perspective of arithmetic aggregation and geometric aggregation respectively. Additionally, we establish a decision-making method based on the proposed aggregation operators. Finally, the feasibility and reliability of the method is illustrated by two numerical examples.