Decision Algorithm for Interval Valued Intuitionistic Fuzzy Heronian Mean Aggregation Operators Based on Aczel Alsina T-Norm

Multi-Attribute Decision Making (MADM) is a powerful tool for navigating complex decision problems by systematically considering multiple criteria and alternatives. This method is widely used in various fields such as business, engineering, finance, and public policy, where decisions involve considering multiple conflicting objectives. An interval-valued intuitionistic fuzzy set is a more flexible mathematical model used to aggregate vague type and redundant information into a single set. By exploring the robustness of Aczel Alsina aggregation operators, we deduce an effective mathematical approach for handling ambiguous information of human opinion. To express the relationship among input arguments or attribute information, we study a feasible theory of Hamy mean (HM) operators. This article presents some dominant mathematical approaches in the light of interval-valued intuitionistic fuzzy (IVIF) information with Aczel Alsina operations including IVIF Aczel Alsina HM (IVIFAAHM), IVIF Aczel Alsina weighted HM (IVIFAAWHM), IVIF Aczel Alsina Dual HM (IVIFAADHM) and IVIF Aczel Alsina weighted Dual HM (IVIFAAWDHM) operators. To prove the validity and effectiveness of derived approaches, some prominent characteristics are also illustrated. A decision algorithm of the MADM technique is also established to resolve complicated real-life applications and amplifications. With the help of numerical examples, we show the compatibility of diagnosed mathematical approaches. Finally, the influence study and comparison technique also verify the consistency of pioneered approaches by contrasting the aggregated outcomes of previous operators that exist in the literature.