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Fermatean fuzzy sets (FFSs), proposed by Senapati and Yager (2019a), can handle uncertain information more easily in the process of decision making. They defined basic operations over the Fermatean fuzzy sets. Here we shall introduce three new operations: subtraction, division, and Fermatean arithmetic mean operations over Fermatean fuzzy sets. We discuss their properties in details. Later, we develop a Fermatean fuzzy weighted product model to solve the multi-criteria decision-making problem. Finally, an illustrative example of selecting a suitable bridge construction method is given to verify the approach developed by us and to demonstrate its practicability and effectiveness.

In the creation of better multiple attribute decisionmaking (MADM) patterns to address the ambiguity in the expanding sophisticated of expert systems, the hypothesis of interval-valued intuitionistic fuzzy sets has proven to be an effective and advantageous technique. We employ Aczel-Alsina operations to remedy the MADM issue, wherein all data supplied by decisionmakers is conveyed as interval-valued intuitionistic fuzzy (IVIF) decision matrices with all components described by an IVIF number (IVIFN). This allows us to satisfy much more demands from fuzzy decisionmaking concerns (IVIFN). In the framework of IVIFNs, we primarily describe several novel Aczel-Alsina operations. On the basis of these operations, we construct several novel IVIF aggregation operators, such as the IVIF Aczel-Alsina weighted averaging operator, the IVIF Aczel-Alsina order weighted averaging operator, and IVIF Aczel-Alsina hybrid averaging operator. We built up several features of such operators. We recommend an MADM technique dependent on the advanced IVIF aggregation operators.To demonstrate the effectiveness of the developed technique, we present an overview of research scientist