Development of the hesitant fuzzy weighted averaging–geometricaggregation operator (HFW-AG) under hesitant fuzzy information

Abstract

The hesitant fuzzy set (HFS) framework has been widely used in multi-criteria group decision-making (MCGDM) to represent uncertainty and hesitation in decision-makers' assessments. However, existing hesitant fuzzy aggregation operators often rely solely on either averaging or geometric aggregation mechanisms, which may limit their ability to capture different characteristics of hesitant fuzzy information. To address this issue, this study proposes a new hesitant fuzzy weighted averaging--geometric aggregation (HFW-AG) operator that combines the features of weighted averaging and geometric aggregation within a unified framework. Several mathematical properties of the proposed operator, including boundedness, monotonicity, and idempotency, are established to demonstrate its theoretical validity. Furthermore, an MCGDM procedure based on the HFW-AG operator is developed for decision-making under hesitant fuzzy environments. A numerical example is presented to illustrate the implementation of the proposed approach, and comparative analyses are conducted with the existing hesitant fuzzy weighted averaging (HFWA) and hesitant fuzzy weighted geometric (HFWG) operators. The results show that the HFW-AG operator exhibits a distinct aggregation behavior and produces a different ranking pattern of alternatives, reflecting its ability to capture hesitant fuzzy information from both additive and multiplicative perspectives. These findings demonstrate the applicability of the proposed operator and its potential usefulness for MCGDM problems involving uncertainty and ambiguity..