As a fuzzy set (FS) expansion, the hesitant fuzzy set (HFS) is successfully employed to demonstrate circumstances where it is admissible to ascertain a few potential membership degrees (MDs) of a component in a set because of the uncertainty between various values. Considering that there is still no research on Aczel–Alsina triangular norms and conorms in a hesitant fuzzy (HF) environment, in this article we introduce for the first time, Aczel–Alsina operations on HFSs. Then, based on these operations, we originate a few new aggregation operators for aggregating HF information namely HF Aczel–Alsina weighted averaging (HFAAWA) operator, HF Aczel–Alsina ordered weighted averaging (HFAAOWA) operator, HF Aczel–Alsina hybrid averaging (HFAAHA) operator, HF Aczel–Alsina weighted geometric (HFAAWG) operator, HF Aczel–Alsina ordered weighted geometric (HFAAOWG) operator, HF Aczel–Alsina hybrid geometric (HFAAHG) operator and HF Aczel–Alsina weighted Bonferroni mean (HFAAWBM) operator. Some essential characteristics of those suggested operators are shown, and the interrelatedness between them is displayed exhaustively. Then, we take advantage of those operators to produce a methodology to interpret the HF multiple attribute decision making (MADM) difficulties. We present a functional model for cyclone disaster assessment to certify the produced approaches and to establish their effectiveness and practicality. Further, we conduct comparison analysis for the legitimacy of our produced methodologies.
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