The q-rung orthopair fuzzy-valued neutrosophic sets: Axiomatic properties, aggregation operators and applications

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.