A Hybrid Probabilistic-Neutrosophic Adaptive Convergence Model for Analyzing Innovative Performance of Agricultural Technology Enterprises in the Digital Economy

Abstract

 This paper introduces a novel mathematical framework that integrates hybrid 
probabilistic-neutrosophic logic with adaptive rough ideal statistical convergence (AR-I
st) to model and analyze the dynamic performance of innovative agricultural technology 
enterprises within the digital economy. Unlike classical convergence approaches, the 
proposed model operates within a neutrosophic normed space (NNS) that accounts for 
truth, indeterminacy, and falsity dimensions, enabling the representation of complex, 
uncertain, and partially known data. By embedding a tri-valued probabilistic 
distribution—comprising the likelihood of growth (T), uncertainty (I), and decline (F) we 
define a new form of convergence, namely Hybrid Probabilistic-Neutrosophic 
Convergence (HPNC). Simultaneously, we formulate adaptive mechanisms for the 
convergence parameters r,λ,ϵ r, allowing the model to dynamically respond to evolving 
enterprise behavior over time. Applied to the context of digital agricultural innovation 
firms, our framework captures the non-linear and uncertain trajectories of technological 
diffusion, resource allocation, and innovation stability. The resulting model is not merely 
theoretical but structurally mirrors the adaptive complexity of real-world agri-tech 
ecosystems. Key properties such as closedness, convexity, and boundedness of the 
convergence sets are proven, establishing the robustness of the approach.

DOI: 10.5281/zenodo.16498066