Development <italic>p</italic>, <italic>q</italic>, <italic>r</italic>&#x2013;Spherical Fuzzy Einstein Aggregation Operators: Application in Decision-Making in Logo Design

Abstract

$p,q,r-$ spherical fuzzy ( $p,q,r-$ SF) sets are a significant advancement in fuzzy set (FS) theory, providing an effective way to describe hesitation inside a set. This development goes beyond membership degrees (MDs) by incorporating three parameters (p, q and r) that shape and define the spread of FS. The presence of these parameters makes $p,q,r-$ SF sets ideal for dealing with complicated decision-making (DM) scenarios in a wide range of applications. In this paper, we proposed a new reliable method for smart DM in logo design projects that uses $p,q,r-$ SF Einstein aggregation operators (AOs). First, we present the $p,q,r-$ SF Einstein operators, which are accomplished of capturing the relationship and interrelationship of numerous criteria while making decisions on logo design, including originality, relevance, beauty, and usability. Next, we use the proposed framework, a multi-criteria decision analysis tool, to rank the choices. We demonstrate the practical application and efficiency of our method in a scenario in which a team of three designers is entrusted with developing five different logo styles for diverse enterprises. Moreover, we compare proposed procedure with some existing methods, demonstrating its advantages in terms of precision and reliability.

Keywords

• p, q, r–spherical fuzzy set
• Einstein operations
• aggregation operators
• decision-making
• optimization