Extended CODAS method for MAGDM with $2$-tuple linguistic $T$-spherical fuzzy sets

In the literature, extensions of common fuzzy sets have been proposed one after another. The recent addition is spherical fuzzy sets theory, which is based on three independent membership parameters established on a unit sphere with a restriction linked to their squared summation. This article uses the new extension that presents bigger domains for each parameter for production design. A systematic approach for determining customer demands or requirements, Quality Function Deployment (QFD) converts them into the final production to fulfill these demands in a decision-making environment. In order to prevent information loss during the decision-making process, it offers a useful technique to describe the linguistic analysis in terms of 2-tuples. This research introduces a novel decision-making method utilizing the 2-tuple linguistic $T$-spherical fuzzy numbers (2TL $T$-SFNs) in order to select the best alternative to manufacturing a linear delta robot. Taking into account the interaction between the attributes, we develop the 2TL $T$-SF Hamacher (2TL $T$-SFH) operators by using innovative operational rules. These operators include the 2TL $T$-SFH weighted average (2TL $T$-SFHWA) operator, 2TL $T$-SFH ordered weighted average (2TL $T$-SFHOWA) operator, 2TL $T$-SFH hybrid average (2TL $T$-SFHHA) operator, 2TL $T$-SFH weighted geometric (2TL $T$-SFHWG) operator, 2TL $T$-SFH ordered weighted geometric (2TL $T$-SFHOWG) operator, and 2TL $T$-SFH hybrid geometric (2TL $T$-SFHHG) operator. In addition, we discuss the properties of 2TL $T$-SFH operators such as idempotency, boundedness, and monotonicity. We develop a novel approach according to the CODAS (Combinative Distance-based Assessment) model in order to deal with the problems of the 2TL $T$-SF multi-attribute group decision-making (MAGDM) environment. Finally, to validate the feasibility of the given strategy, we employ a quantitative example to select the best alternative to manufacture a linear delta robot. The suggested information-based decision-making methodology which is more extensively adaptable than existing techniques prevents the risk of data loss and makes rational decisions.