T-spherical fuzzy (T-SF) sets deal with degrees of belongingness, abstinence, and non-belongingness which make them superior in comparison to fuzzy sets and intuitionistic fuzzy sets. In any group decision-making process, the experts’ judgments include ambiguity and uncertainty, particularly in selecting alternatives based on a given collection of criteria. The existing research on T-SF sets do not focus on both the subjective and objective weights. Consequently, the outcomes get distorted. To tackle this situation, in this work, we utilize the concepts of consistency and similarity between the decision experts so as to determine the decision experts’ subjective and objective weights, respectively, under the T-SF environment. For the purpose of aggregation, T-SF weighted Copula aggregation operators are developed to avoid loss of information. We discuss the elegant properties of these proposed aggregation operators. We provide a case study regarding open-source software LMS selection to focus on the practicability and usefulness of the proposed approach.