r, s, t-Spherical Fuzzy VIKOR Method and Its Application in Multiple Criteria Group Decision Making

This study intends to significantly enhance the capacity of decision experts (DEs) to capture their judgment in a larger area. In order to accomplish this, we propound the $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy set ( $\textsf {r},\textsf {s},\textsf {t}$ -SFS), an expansion of the t-spherical fuzzy set. In $\textsf {r},\textsf {s},\textsf {t}$ -SFS the sum of the $\textsf {r}$ th power of membership grade, $\textsf {s}$ th power of neutral grade and the $\textsf {t}$ th power of non-membership grade is less than or equal to 1, where $\textsf {r}$ , $\textsf {s}$ and $\textsf {t}$ are natural numbers. Due to the inclusion of the extra parameters $\textsf {r}$ and $\textsf {s}$ , the $\textsf {r},\textsf {s},\textsf {t}$ -SFS is able to describe assessment information in a more flexible and comprehensive manner. This work begins by defining $\textsf {r},\textsf {s},\textsf {t}$ -SFS and demonstrating that it is an extension of various existing fuzzy sets. The fundamental operations, score, and accuracy functions of $\textsf {r},\textsf {s},\textsf {t}$ -SFS are then introduced, and their mathematical features are examined. Also, we study some distance measures between $\textsf {r},\textsf {s},\textsf {t}$ -SFSs and their required properties. Next, to aggregate $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy data, $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy weighted averaging ( $\textsf {r},\textsf {s},\textsf {t}$ -SFWA) and $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy weighted geometric ( $\textsf {r},\textsf {s},\textsf {t}$ -SFWG) operators are bring forward along with some of their essential properties. Based on the proposed distance measure, maximizing deviation method is combined with $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy information to establish the criteria weight determination method. Following this, we present $\textsf {r},\textsf {s},\textsf {t}$ -spherical fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method using the grounds of classical VIKOR method depending upon two focal properties, namely, group utility and individual regret of opponent. To demonstrate the use of the framed approach and exhibit its validity, we present a case study of arc welding robot selection. Besides, the effectiveness and accuracy of the proposed VIKOR are proved by parameter analysis and comparison analysis findings.