Numerical solution of interval-valued trapezoidal fuzzy non-linear system of equations and its applications

Abstract

In many areas of applied mathematics, physical and chemical sciences, and engineering sciences-particularly bio engineering-the topic of fuzzy systems of nonlinear equations with an interval-valued trapezoidal fuzzy (IVTF) number or crisp real-valued coefficient matrix and with a vector of interval-valued trapezoidal fuzzy numbers or crisp real value numbers on the right-hand side arises. However, insufficient investigation has been made into the development and assessment of numerical schemes for resolving interval value trapezoidal fuzzy nonlinear systems of equations (IVTFNSEs). In this paper, we develop and analyzes efficient higher order IVTF-numerical schemes for solving IVTFNSEs. Supply chain networks with unpredictable needs and IVTF data are taken into consideration for some problems in econometrics. Numerical examples using interval-valued trapezoidal fuzzy quantities in the parametric form are explored. The outcomes of numerical methods are tested using various stopping criteria, then compared and analyzed with other existing methods on the basis of computational CPU time in seconds, local errors, maximum errors, residual errors and consistency. The numerical outcomes frequently demonstrate that our newly developed method performs better than existing classical techniques, obtaining higher accuracy, faster convergence, and lower computing cost. The graphical findings are analyzed in order to demonstrate and support the theoretical significance, illustrating the better performance of the newly modified numerical techniques over the existing numerical scheme. The suggested approach for solving trapezoidal fuzzy nonlinear systems is a useful tool for real-world applications involving uncertainty and complex systems, since these results confirm its robustness, efficiency, and applicability.