Modeling Entangled Indeterminacy Flows: A Neutrosophic Multi Module Simulation Framework for Cross-Border E-Commerce Digital Marketing Effectiveness

Abstract

In contemporary cross-border e-commerce, decision-making is challenged not only by 
randomness but also by interdependent layers of indeterminacy arising from fragmented 
regulations, incomplete market intelligence, and volatile logistical conditions. Traditional 
neutrosophic probability frameworks treat the indeterminate component I as an 
independent attribute of each variable, neglecting possible structural interdependencies 
across system components. This paper introduces the Neutrosophic Entangled 
Indeterminacy Flow Model (NEIFM), a novel simulation-based approach that captures 
the propagation and transformation of interlinked indeterminacy within multi-module 
marketing systems. Using a Design Structure Matrix (DSM) and N² diagram architecture, 
each module in the simulation represents a functional domain such as advertising 
performance, customer conversion rates, customs regulations, shipping logistics, and 
currency exchange impacts, characterized by a neutrosophic triple (T, I, F). An 
Entanglement Matrix is proposed to quantify the mutual influence of I values among 
modules, allowing the model to update indeterminacy levels dynamically as simulation 
cycles progress. This framework enables marketers and strategists to identify critical 
nodes where entangled indeterminacy amplifies risk, thereby providing actionable 
insights for targeted intervention. A  numerical case study demonstrates the mathematical 
formulation, simulation process, and strategic implications of NEIFM, marking the first 
integration of entangled indeterminacy into neutrosophic probability theory and 
multidisciplinary system simulation for e-commerce marketing.

DOI: 10.5281/zenodo.16887788