Confidence Levels-Based <italic>p</italic>, <italic>q</italic>, <italic>r</italic>&#x2013;Spherical Fuzzy Aggregation Operators and Their Application in Selection of Solar Panels

Abstract

${p,q,r}$ –spherical fuzzy sets are an extension of picture fuzzy, spherical fuzzy and t-spherical fuzzy sets, which allow for a more flexible representation of uncertainty. In a $p,q,r$ –spherical fuzzy set, decision makers have the flexibility to adjust the influence of membership grades simultaneously by integrating parameters p, q, and r, enabling them to manage the impact of these grades effectively. In this setting, while considering the confidence levels associated with each $p,q,r$ –spherical fuzzy number ( $p,q,r$ –SFN), the current study explored novel averaging and geometric operators known as confidence $p,q,r$ –spherical fuzzy weighted averaging $({C_{p,q,r}}SFWA)$ and confidence $p,q,r$ –spherical fuzzy weighted geometric $({C_{p,q,r}}SFWG)$ , along with their associated desirable properties. Subsequently, a multi-criteria decision-making (MCDM) method is proposed and demonstrated through an example related to the selection of best solar panels to validate its soundness and effectiveness. The computed results are then compared with some existing approach to further support the outcomes of the proposed work.

Keywords

• p, q, r–spherical fuzzy sets
• aggregation operators
• confidence levels
• decision making
• optimization