On Solving Linear Complementarity Problem using Principal Pivoting Method

Objectives: A rudimentary framework called the linear complementarity problem (LCP) describes a wide range of real-world scenarios in which equilibrium conditions must be met while adhering to constraints. Methods: This study presents the Principal Pivoting Method (PPM), a novel method for solving linear Complementarity problems. PPM is a viable substitute for addressing large-scale complementarity problems. It is a powerful method for handling large-scale challenge circumstances while addressing LCPs. The PPM uses a principle-based pivoting strategy to navigate the solution space. It terminates in a finite number of iterations. It deals with degenerate cases. Findings: Under specific hypotheses, the PPM is guaranteed to converge to a solution if one exists. PPM's pivoting methods account for its numerical stability. In this paper, the process is analyzed using real-life scenarios. The algorithm goes with initialization, iteration, and termination. To ensure numerical stability, a pivot element is selected. Update the basis matrix through pivotal operations. The iterations show how well the algorithm goes perfectly without causing any wrongdoing. Using this method, the solution is obtained accurately in a smaller number of iterations. Novelty: A novelty of the work is finding a solution to a real-life application problem using this method. The comparison of my research work with the existing research work is a novel approach to illustrate the Principal Pivoting method in practical applications. Here, the crisp values are converted into intuitionistic triangular fuzzy numbers for analyzing data in real-life scenarios. This is a novel way to attempt a newly considered problem, which is taken as fuzzy coefficients transforming into a linear complementarity problem. Fuzzy arithmetic operations on the Function principle are utilized. The numerical trials proved the efficacy of the suggested algorithm. Keywords: Fuzzy Linear Complementarity Problem (FLCP), Principle Pivoting Method (PPM), Intuitionistic Fuzzy set (IFS), Triangular Intuitionistic Fuzzy Number (TIFN)