Enhanced representation of uncertain data: integration of interval-valued neutrosophic numbers and virtual logic with parameterization tool

This paper presents the development of a novel parameterization framework within the theory of soft sets to model and structure complex data in uncertain environments. A new hybrid set type, called the virtual interval-valued neutrosophic parametrized soft (vivnp-s-)set, is proposed to address the limitations of existing uncertainty handling models. The vivnp-s-set integrates interval-valued neutrosophic numbers, known for effectively expressing multi-dimensional membership degrees, with the concept of virtual logic, which reduces human-induced inconsistencies in decision-making. This integration enables a more precise and flexible representation of uncertainty. The paper rigorously constructs the theoretical foundations of vivnp-s-sets, including their basic set operations, properties, and transformations, thereby establishing a comprehensive mathematical structure. Furthermore, an algorithm based on the vivnp-s-set framework is proposed, incorporating parameter reduction methods to improve efficiency in complex decision-making scenarios. Comparative analyses demonstrate that the proposed approach not only generalizes existing hybrid models but also enhances decision accuracy and interpretability under indeterminate conditions. The findings highlight the novelty and applicability of the vivnp-s-set model as a robust tool for representing and processing uncertain information across diverse domains.