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.

When dealing with the haziness that is intrinsic in decision analysis-driven decision making procedures, interval-valued intuitionistic fuzzy sets (IVIFSs) can be quite effective. Our approach to solving the multiple attribute decision making (MADM) difficulties, where all of the evidence provided by the decision-makers is demonstrated as interval-valued intuitionistic fuzzy (IVIF) decision matrices, in which all of the components are distinguished by an IVIF number (IVIFN), is based on Aczel–Alsina operational processes. We begin by introducing novel IVIFN operations including the Aczel–Alsina sum, product, scalar multiplication, and exponential. We may then create IVIF aggregation operators, such as the IVIF Aczel–Alsina weighted geometric operator, the IVIF Aczel–Alsina ordered weighted geometric operator, and the IVIF Aczel–Alsina hybrid geometric operator, among others. We present a MADM approach that relies on the IVIF aggregation operators that have been developed. A case study is used to demonstrate the practical applicability of the strategies proposed in this paper. By contrasting the newly developed technique with existing techniques, the method is capable of demonstrating the advantages of the newly developed approach. A key result of this work is the discovery that some of the current IVIF aggregation operators are subsets of the operators reported in this article.