This article presents a novel study of spherical fuzzy sets (SFSs), a more comprehensive framework of intuitionistic fuzzy sets and picture fuzzy sets. The SFS allows the decision-makers (DMs) to cope with complicated and insufficient information during the aggregation process. The Heronian mean (HrM) model theory is also utilized to express correlation among different input arguments or characteristics. Recently, the theory of Aczel Alsina triangular norms gained a lot of attention from various research scholars and has many capabilities to provide smooth approximations during decision analysis. In this article, we developed some appropriate operations of Aczel Alsina t-norms and t-conorms in light of spherical fuzzy (SF) information. We develop new mathematical ways to look at SF data to keep clarity and sufficient information. These are the SF Aczel Alsina Heronian mean (SFAAHrM) and SF Aczel Alsina weighted Heronian mean (SFAAWHrM) operators. Furthermore, we also present a list of new strategies based on Aczel Alsina operations, such as SF Aczel Alsina geometric Heronian mean (SFAAGHrM) and SF Aczel Alsina weighted geometric Heronian mean (SFAAWGHrM) operators. Some notable properties are also characterized to show the validity and effectiveness of our derived mathematical approaches. Considering our derived strategies, an algorithm for the multiple attribute decision-making (MADM) problem is established to resolve complicated real-life applications. A numerical example presents the compatibility of derived approaches and provides a solid mechanism to improve the performance of educational institutes. A comparison technique is also demonstrated to show the applicability and consistency of diagnosed approaches by contrasting the findings of pioneered approaches with existing methodologies.
Keywords: Aczel Alsina aggregation operations; And decision support system; Heronian mean models; Spherical fuzzy set values.
© 2024 The Authors.