Enhancing the Aczel–Alsina Model: Integrating Hesitant Fuzzy Logic with Chi-Square Distance for Complex Decision-Making

The paper presents an innovative method for tackling multi-attribute decision-making (MADM) problems within a hesitant fuzzy (HF) framework. Initially, the paper generalizes the Chi-square distance measure to the hesitant fuzzy context, defining the HF generalized Chi-square distance. Following this, the paper introduces the power average (P-A) operator and the power geometric (P-G) operator to refine the weights derived from Shannon entropy, taking into account the inter-attribute support. Leveraging the strengths of Aczel–Alsina operations and the power operation, the paper proposes the hesitant fuzzy Aczel–Alsina power weighted average (HFAAPWA) operator and the hesitant fuzzy Aczel–Alsina power weighted geometric (HFAAPWG) operator. Consequently, a hesitant fuzzy Aczel–Alsina power model is constructed. The applicability of this model is demonstrated through a case study examining the urban impacts of cyclonic storm Amphan, and the model’s superiority is highlighted through comparative analysis.