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 r, s, t-spherical fuzzy set (r, s, t-SFS), an expansion of the t-spherical fuzzy set. In r, s, t-SFS the sum of the rth power of membership grade, sth power of neutral grade and the tth power of non-membership grade is less than or equal to 1, where r, s and t are natural numbers. Due to the inclusion of the extra parameters r and s, the r, s, t-SFS is able to describe assessment information in a more flexible and comprehensive manner. This work begins by defining r, s, t-SFS and demonstrating that it is an extension of various existing fuzzy sets. The fundamental operations, score, and accuracy functions of r, s, t-SFS are then introduced, and their mathematical features are examined. Also, we study some distance measures between r, s, t-SFSs and their required properties. Next, to aggregate r, s, t-spherical fuzzy data, r, s, t-spherical fuzzy weighted averaging (r, s, t-SFWA) and r, s, t-spherical fuzzy weighted geometric (r, s, 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 r, s, t-spherical fuzzy information to establish the criteria weight determination method. Following this, we present r, s, 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.

The p,q -quasirung orthopair fuzzy set ( p,q -ROFS) is a potent tool for representing fuzziness and uncertainty compared to the q -rung orthopair fuzzy set (q-ROFS). This research aims to introduce the aggregation technique of p,q -ROFSs with the help of Aczel–Alsina (AA) operations. We first propound several novel AA operations of p,q -ROFSs such as AA sum, AA product, AA scalar multiplication, and AA exponentiation. Following these operations, we develop a range of p,q -quasirung orthopair fuzzy averaging and geometric aggregation operators to efficiently aggregate p,q -quasirung fuzzy data. Additionally, we construct different features of these operators, discuss certain special cases, and study their fundamental results. Afterward, we use these operators to design a method for dealing with multi-criteria decision-making with p,q -quasirung orthopair fuzzy information. Finally, we provide a case study to demonstrate the suggested method’s practicality followed by parameter analysis and comparison study.