On Globular T‐Spherical Fuzzy Sets With Weighted Aggregation Operators and Application to Multicriteria Group Decision‐Making

In this paper, we give the concept of novel globular T‐spherical fuzzy sets (G‐TSFSs) as an innovative extension of TSFSs and circular spherical fuzzy sets (C‐SFSs). G‐TSFSs represent membership, indeterminacy, and nonmembership degrees using a globular/sphere bound that can offer a more accurate portrayal of vague, ambiguous, and imprecise information. By employing a structured representation of data points on a sphere with a specific center and radius, this model enhances decision‐making processes by enabling a more comprehensive evaluation of objects within a flexible region. Following the newly defined G‐TSFSs, we establish some basic set operations and introduce fundamental algebraic operations for G‐TSF values (G‐TSFVs). These operations expand the evaluative capabilities of decision‐makers, facilitating more sensitive decision‐making processes in a broader region. To quantify a similarity measure (SM) between G‐TSFVs, the SM is defined based on the radius of G‐TSFSs. Additionally, Hamming and Euclidean distances are introduced for G‐TSFSs. We also present theorems and examples to elucidate computational mechanisms. Furthermore, we give the G‐TSF weighted average (G‐TSFWA) and G‐TSF weighted geometric (G‐TSFWG) operators. Leveraging our proposed SM, a multicriteria group decision‐making (MCGDM) scheme for G‐TSFSs, named G‐TSF MCGDM (G‐TSFMCGDM), is developed to address group decision‐making problems. The applicability and effectiveness of the proposed G‐TSFMCGDM method are demonstrated by applying it to solve the selection problem of the best venue for professional development training sessions in a firm. The analysis results affirm the suitability and utility of the proposed method for resolving MCGDM problems, establishing its effectiveness in practical decision‐making scenarios.