Neutrosophic Rings for Modeling and Optimizing Cross-Border E Commerce Digital Marketing Campaigns

Abstract

This paper presents a new symbolic mathematical structure called the 
Neutrosophic Evaluation Ring (NER) for assessing the effectiveness of digital marketing 
in cross-border e-commerce environments. The model is built upon a neutrosophic triplet 
system, where each marketing campaign is represented by a three-component element 
that reflects degrees of persuasiveness, uncertainty, and rejection. These components 
interact under custom-defined binary operations that satisfy the axioms of a commutative 
ring with neutrosophic characteristics. By introducing specialized addition and 
multiplication operations within this ring, the model captures the real-world behaviors of 
marketing messages as they are perceived differently across cultural and linguistic 
boundaries. The ring structure enables logical manipulation of marketing states while 
preserving the interactions between clarity, ambiguity, and opposition. The paper 
establishes the mathematical foundation of the proposed ring, proves its key properties, 
and provides full numerical examples that illustrate its utility. A detailed case study 
simulates marketing performance across three international markets, demonstrating how 
the ring framework can detect unstable regions in campaign strategies and reveal hidden 
layers of customer interpretation. The proposed model offers a rigorous and adaptive way 
to evaluate digital campaigns under the complex, uncertain conditions of global e
commerce. 

DOI: 10.5281/zenodo.15825624