The primary aim of this study is to address potential inaccuracies in membership values expressed by decision-makers when dealing with uncertainty in complex environments. To achieve this, the concept of virtual logic is incorporated as a refinement mechanism. Building on this foundation, we construct the notion of a virtual fuzzy parameterized fuzzy hypersoft set (vfp-fhs-set) by integrating virtual logic with hypersoft sets, which are designed to more effectively represent the components of parameter sets. Through this integration, a novel hybrid mathematical model is introduced, enhancing parameterization with fuzzy membership values and providing a more robust framework for decision-making under uncertainty. Several fundamental set operations associated with this structure are formally examined to establish its theoretical soundness. Furthermore, a decision-making algorithm based on vfp-fhs-sets is proposed and illustrated with an application, demonstrating the practical utility of the model. Comparative analysis with existing approaches highlights the advantages of incorporating virtual logic, particularly in improving precision and reliability in the ranking of alternatives.
Orhan Dalkılıç (Sun,) studied this question.