فهرست نشریات علمی دسترسی آزاد ایران

The Linear Complementarity Problem (LCP) is a cornerstone in optimization, game theory, and variational inequalities. Existing fuzzy and neutrosophic extensions improve uncertainty handling, but they often lack a structured formulation that ensures solvability and interpretability. To fill this gap, we develop a novel framework based on Neutrosophic Structured Elements (NSEs). Unlike previous approaches, the proposed Neutrosophic LCP (NLCP) embeds triangular single-valued neutrosophic numbers (TSVNNs) into structured monotonic functions over [−1, 1], enabling consistent arithmetic, inequalities, and complementarity conditions. We further design two computational algorithms, namely the N-Lemke and N-Pivot methods, which provide dual algorithmic strategies for solving NLCPs. Theoretical properties such as existence, uniqueness, and reduction to the classical LCP are established. Numerical experiments, including both small and mid-scale test cases, demonstrate the practicality and scalability of the approach, highlighting its advantages over classical, fuzzy, and conventional neutrosophic LCP methods.