Eye Lens Evaluation: Unpacking Performance, Comfort, and Cost through Fermatean Fuzzy Z-Numbers

In this research paper, a comprehensive evaluation of eye lenses is conducted, focusing on three key criteria: performance, comfort, and cost. However, to minimize the chances of large errors attributable to the vagueness and subjectivity of the approach, the Fermatean fuzzy Z-number approach should be employed because it enhances the accuracy of decision-making as it combines the level of uncertainty of the information with the credibility of the opinion of the expert. Moreover, second-order Fermatean fuzzy Z-number weighted averaging and geometric operations are used to fuse the experts’ assessments, which arrive at different aspects. The present paper also defines some basic properties based on Fermat fuzzy Z-numbers and their proofs. To justify the credibility of the results that emerged from the proposed aggregation operators and those of the combined compromise solution method, similar and compromise-similar results were obtained by using the weighted averaging and geometric aggregation to pool the expertise evaluation over multiple attributes. Also, some fundamental properties dependent on Fermat fuzzy Z-numbers and their corresponding proofs are discussed. To overcome this issue and enhance the validity of this research, the results of the proposed aggregation operators have been checked with the combined compromise solution method and found similar outcomes. This paper demonstrates that these modern fuzzy-based methods are suitable for the required structural and balanced ranking of lenses while also providing information about the optimal eye lenses based on various criteria. Besides improving lens assessment capacity, this method also demonstrates the applicability of Fermatean fuzzy Z-numbers in decision-making, which are advantageous for consumers and optical industry professionals.