A bipolar complex fuzzy credibility set (BCFCS) is a new approach in computational intelligence and decision-making under uncertainty. Bipolar complex fuzzy credibility (BCFC) information has been employed as a strategy for dealing with confusing and unreliable situations that arise in everyday life. In this paper, we used the concept of aggregation operators to diagnose the well-known averaging and geometric aggregation operators, as well as evaluate some properties and related results. Using described operators, an algorithm for multiple criteria group decision making is proposed. Then, a numerical example of a case study of Hospital selection is discussed. Lastly, the comparative analysis of suggested operators with existing operators are also given to discuss the rationality, efficiency and applicability of these operators.

The idea of sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs), which allows more uncertainty than fractional orthotriple fuzzy sets (FOFSs) is noteworthy. The regularity and symmetry of the origin are maintained by the widely recognized sine hyperbolic function, which satisfies the experts' expectations for the properties of the multi-time process. Compared to fractional orthotriple linear Diophantine fuzzy sets, sine hyperbolic fractional orthotriple linear Diophantine fuzzy sets (sinh-FOLDFSs) provide a significant idea for enabling more uncertainty. The objective of this research is to provide some reliable sine hyperbolic operational laws for FOLDFSs in order to sustain these properties and the significance of sinh-FOLDFSs. Both the accuracy and score functions for the sinh-FOLDFSs are defined. We define a group of averaging and geometric aggregation operators on the basis of algebraic t-norm and t-conorm operations. The basic characteristics of the defined operators are studied. Using the specified aggregation operators, a group decision-making method for solving real-life decision-making problem is proposed. To verify the validity of the proposed method, we compare our method with other existing methods.

Linguistic complex intuitionistic fuzzy aggregation operators are a novel idea for the description of intuitionistic fuzzy information, where linguistic complex concepts are used to describe membership and non-membership. This can convey the hazy information more clearly, and some findings on linguistic complex intuitionistic fuzzy aggregation operators have been attained. Nonetheless, several linguistic complex intuitionistic fuzzy aggregation operators in the literature are founded on conventional operational principles, which have certain limitations when used to multi-attribute group decision-making (MAGDM). In this study, we presented some improved operating rules based on linguistic complex intuitionistic fuzzy variables (LCIFVs) and changed their features to address these issues. Next, we created a few aggregation operators, such as the enhanced linguistic complex intuitionistic fuzzy weighted average (LCIFWA) and the linguistic complex intuitionistic fuzzy ordered weighted averaging (LCIFOWA) operator, to fuse the decision information represented by LCIFVs. We also demonstrated that they had a few favorable qualities. We introduced many novel approaches to address the MAGDM issues in the context of the linguistic complex intuitionistic fuzzy environment, based on the LCIFOWA and linguistic complex intuitionistic fuzzy ordered weighted geometric (LCIFOWG) operators. In short, we employed few real-world scenarios to demonstrate the viability and soundness of the suggested techniques through comparison with other approaches. This unique technique has been applied to plastic waste management selection, and the results are more accurate than the previously used materials and methods.