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

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.