HESITANT TRIANGULAR FUZZY GENERALIZEDGEOMETRIC HERONIAN MEAN:AN ADVANCED MCDM APPROACH

Abstract

Uncertainty and hesitation are common challenges in real world
multi criteria decision making (MCDM) problems, where evaluations often involve vague, imprecise, or incomplete information. This is especially important in areas such as healthcare, supply chain management and sustainability, since there is often uncertainty in the advice offered by experts.
Traditional aggregation methods, such as the Generalized Geometric Heronian Mean (GGHM), typically rely on precise numerical data and therefore struggle to represent the ambiguity inherent in expert judgments. To address this limitation, this study introduces a novel aggregation operator, the Hesitant Triangular Fuzzy Generalized Geometric Heronian Mean (HTFGGHM), which integrates hesitant triangular fuzzy sets (HTFs) to better capture uncertainty and hesitation in evaluations. The proposed operator
accommodates multiple membership degrees for each input, allowing for a more realistic and flexible aggregation process. The theoretical formulation and essential properties of the HTFGGHM operator are rigorously examined. The numerical example shows that the operator is capable of finding the same best option regardless of the settings. In addition, a sensitivity analysis is performed to evaluate its robustness and stability under different decision making conditions, demonstrating its effectiveness in handling complex and uncertain MCDM scenarios.