A Neutrosophic Topological and Algebraic Model for Evaluating Venture Capital Performance in Small and Medium-Sized Technology Enterprises

Abstract

This paper presents a new mathematical model for analyzing venture capital 
(VC) decisions in small and medium-sized technology enterprises (SMEs). The model is 
based on two novel neutrosophic structures. First, we introduce the Neutrosophic Risk 
Topological Space (NRTS), which represents the uncertainty, trust, and risk in VC 
decision-making using a special type of topological structure. This space captures the 
changing nature of technology startups by allowing each possible decision state to be 
measured in terms of truth, indeterminacy, and falsity. Second, we develop the 
Neutrosophic Bi-LA Venture Capital Algebra (NBVC), an algebraic system that models 
interactions between investors and startup projects. The NBVC framework uses two 
binary operations to express both agreement and conflict in VC negotiations. Together, 
these two frameworks allow a complete and detailed evaluation of investment scenarios 
under real-world uncertainty. The paper includes mathematical definitions, logical 
proofs, and full calculation examples. Our results show that neutrosophic tools can 
provide deeper insights into VC dynamics and offer more accurate models than 
traditional fuzzy or classical systems.

DOI: 10.5281/zenodo.15873466