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

Authors

  • Rafi Raza
    Faculty of Computer Science and Mathematics, University of Malaysia Terengganu, Kuala Nerus 210300, Malaysia
  • Ahmad Termimi Bin Ab Ghani
    Faculty of Computer Science and Mathematics, University of Malaysia Terengganu, Kuala Nerus 210300, Malaysia
  • Iraq T. Abbas
    College of Science, Department of Mathematics, University of Baghdad, Baghdad 10071, Iraq
  • Lazim Abdullah
    Faculty of Computer Science and Mathematics, University of Malaysia Terengganu, Kuala Nerus 210300, Malaysia

Keywords:

Hesitant fuzzy sets, Multi-criteria group decision-making, Aggregation operator, HFW-AG operator

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..

Dimensions

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fig 1

Published

2026-08-05

How to Cite

Development of the hesitant fuzzy weighted averaging–geometricaggregation operator (HFW-AG) under hesitant fuzzy information. (2026). African Scientific Reports, 5(2), 491. https://doi.org/10.46481/asr.2026.5.2.491

Issue

Volume 5, Issue 2, August 2026

Section

MATHEMATICAL SCIENCES SECTION
Copyright & Licensing

Copyright (c) 2026 Rafi Raza, Ahmad Termimi Bin Ab Ghani, Iraq T. Abbas, Lazim Abdullah

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Development of the hesitant fuzzy weighted averaging–geometricaggregation operator (HFW-AG) under hesitant fuzzy information. (2026). African Scientific Reports, 5(2), 491. https://doi.org/10.46481/asr.2026.5.2.491

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