A SuperHyperNeutrosophic Statistical Model for Interaction Design in Virtual Reality Art

Abstract

-This paper introduces a novel mathematical framework that integrates 
SuperHyperUncertain and Neutrosophic statistical theories into the domain of interaction 
design within virtual reality (VR) art. Building on advanced (m, n)-SuperHyperFunctions 
and the subset-valued nature of Neutrosophic degrees, we develop a multi-layered 
statistical system capable of modeling hyper-complex user interactions and perceptual 
uncertainties in immersive digital environments. The proposed model captures nuanced 
emotional and cognitive responses to VR art by employing generalized uncertainty 
mappings beyond traditional [0,1] intervals, including over-, under-, and off-probabilistic 
values. We present new definitions, multiple theoretical proofs, and numerical examples 
that demonstrate the system’s effectiveness in representing aesthetic ambiguity and 
interactive feedback in virtual spaces. This study marks the first application of 
SuperHyperNeutrosophic structures to interaction design in VR art, offering a 
mathematically rigorous and conceptually expansive approach to digital media analysis. 

DOI: 10.5281/zenodo.15558352