During the transitional phase spanning from the realm of fuzzy logic to the realm of neutrosophy, a multitude of hybrid models have emerged, each surpassing its predecessor in terms of superiority. Given the pervasive presence of indeterminacy in the world, a higher degree of precision is essential for effectively handling imprecision. Consequently, more sophisticated variants of neutrosophic sets (NSs) have been conceived. The key objective of this paper is to introduce yet another variant of NS, known as the q-rung orthopair fuzzy-valued neutrosophic set (q-ROFVNS). By leveraging the extended spatial range offered by q-ROFS, q-ROFVNS enables a more nuanced representation of indeterminacy and inconsistency. Our endeavor commences with the definitions of q-ROFVNS and q-ROFVN numbers (q-ROFVNNs). Then, we propose several types of score and accuracy functions to facilitate the comparison of q-ROFVNNs. Fundamental operations of q-ROFVNSs and some algebraic operational rules of q-ROFVNNs are also provided with their properties, substantiated by proofs and elucidated through illustrative examples. Drawing upon the operational rules of q-ROFVNNs, the q-ROFVN weighted average operator (q-ROFVNWAO) and q-ROFVN weighted geometric operator (q-ROFVNWGO) are proposed. Notably, we present the properties of these operators, including idempotency, boundedness and monotonicity. Furthermore, we emphasize the applicability and significance of the q-ROFVN operators, substantiating their utility through an algorithm and a numerical application. To further validate and evaluate the proposed model, we conduct a comparative analysis, examining its accuracy and performance in relation to existing models.

The theory of cubic bipolar fuzzy sets (CBFSs) is a robust approach for dealing with vagueness and bipolarity in real-life circumstances. This theory provides a hybrid machine learning paradigm that can accurately describe two-sided contrasting features for medical diagnosis. The ELECTRE-II model, which is extensively used, is expanded in this article to include the cubic bipolar fuzzy (CBF) context. In order to produce a comprehensive preference ordering of actions, ELECTRE-II establishes two different forms of embedded outranking relations while taking into account the subjective human judgments. A huge number of applications have been created by its variations under various models, considering the CBF model's greater capacity to deal. For opinions in the adaptive CBF structure with unknown information, the CBF-ELECTRE-II group decision support method is described. With the use of proper CBF aggregation operations, the expert CBF views on each alternative and criterion are compiled in the first step. The approach then constructs weak and strong outranking relations and offers three distinct CBF outranking set kinds ("concordance", "indifferent" and "discordance" sets). Strong and weak outranking graphs serve as a visual depiction of the latter, which is finally studied by a rigorous iterative procedure that yields a preferred system. For these objectives, integrated CBF-VIKOR and CBF-ELECTRE-II techniques are developed for multi-criteria group decision making (MCDGM). Finally, suggested techniques are recommended to determine ranking index of efficient road freight transportation (FRT) in Industry 4.0. The ranking index and optimal decision are also computed with other techniques to demonstrate robustness of proposed MCDGM approach.

This paper aims to amalgamate the notion of a T-spherical fuzzy set (T-SFS) and a linear Diophantine fuzzy set (LDFS) to elaborate on the notion of the T-spherical linear Diophantine fuzzy set (T-SLDFS). The new concept is very effective and is more dominant as compared to T-SFS and LDFS. Then, we advance the basic operations of T-SLDFS and examine their properties. To effectively aggregate the T-spherical linear Diophantine fuzzy data, a T-spherical linear Diophantine fuzzy weighted averaging (T-SLDFWA) operator and a T-spherical linear Diophantine fuzzy weighted geometric (T-SLDFWG) operator are proposed. Then, the properties of these operators are also provided. Furthermore, the notions of the T-spherical linear Diophantine fuzzy-ordered weighted averaging (T-SLDFOWA) operator; T-spherical linear Diophantine fuzzy hybrid weighted averaging (T-SLDFHWA) operator; T-spherical linear Diophantine fuzzy-ordered weighted geometric (T-SLDFOWG) operator; and T-spherical linear Diophantine fuzzy hybrid weighted geometric (T-SLDFHWG) operator are proposed. To compare T-spherical linear Diophantine fuzzy numbers (T-SLDFNs), different types of score and accuracy functions are defined. On the basis of the T-SLDFWA and T-SLDFWG operators, a multiple attribute decision-making (MADM) method within the framework of T-SLDFNs is designed, and the ranking results are examined by different types of score functions. A numerical example is provided to depict the practicality and ascendancy of the proposed method. Finally, to demonstrate the excellence and accessibility of the proposed method, a comparison analysis with other methods is conducted.