In this paper, we define some Einstein operations on cubic fuzzy set (CFS) and develop three arithmetic averaging operators, which are cubic fuzzy Einstein weighted averaging (CFEWA) operator, cubic fuzzy Einstein ordered weighted averaging (CFEOWA) operator and cubic fuzzy Einstein hybrid weighted averaging (CFEHWA) operator, for aggregating cubic fuzzy data. The CFEHWA operator generalises both the CFEWA and CFEOWA operators. Furthermore, we develop various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. We apply CFEHWA operator to multiple attribute decision-making with cubic fuzzy data. Finally, a numerical example is constructed to demonstrate the established approach.

Decision-making in uncertain and imprecise environments often requires robust mathematical frameworks capable of effectively representing and aggregating conflicting information. Circular Intuitionistic Fuzzy Sets (C-IFSs) are powerful tools for modeling such complexities by combining intuitionistic and cubic fuzzy set properties. In this study, we extend the applicability of C-IFSs by integrating them with the Hamacher operational framework, offering a more flexible and adaptive approach to aggregation. To this end, we propose six novel aggregation operators: Circular Intuitionistic Fuzzy Hamacher Weighted Average (CIFHWA), Circular Intuitionistic Fuzzy Hamacher Ordered Weighted Average (CIFHOWA), Circular Intuitionistic Fuzzy Hamacher Hybrid Weighted Average (CIFHHWA), Circular Intuitionistic Fuzzy Hamacher Weighted Geometric (CIFHWG), Circular Intuitionistic Fuzzy Hamacher Ordered Weighted Geometric (CIFHOWG), and Circular Intuitionistic Fuzzy Hamacher Hybrid Weighted Geometric (CIFHHWG). These operators are designed to address multi-criteria decision-making challenges with improved precision. We further develop score and accuracy functions to rank C-IFSs and propose a neural-based scheme employing cubic correlation coefficients to enhance computational efficiency. A detailed numerical example validates the framework’s effectiveness, illustrating its practical utility. Additionally, comparative analyses with existing techniques and sensitivity and robustness examinations demonstrate its superiority in handling complex decision-making scenarios. The findings underscore the advantages of using Hamacher-based operations with C-IFSs, offering a novel contribution to fuzzy decision-making and opening avenues for future research in uncertain data analysis.

In the present study we have presented the notion of FUZZY BAYESIAN DECISION TECHNIQUE and combined the idea of the Fuzzy TOPSIS technique and entropy. We define the new ideas of fuzzy TOPSIS technique and entropy. So, we introduce the TOPSIS method and entropy, and the weights of the DMs are used. We proposed an MCDM technique based on TOPSIS and entropy. We focus on parameter different solutions of Fuzzy TOPSIS Positive ideal and Negative ideal solutions efficient decision making. Also, we provide a numerical example to elucidate the proposed technique stage by stage. Lastly, we compare the explanations of the current problem with the many existing MCGDM approaches to deliver the skills and rationality of the offered technique. We also provide a sensitivity study by shifting the entropy to establish the weights of the criteria underneath the dominant entropy measure meaning.

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach.