Advanced Fuzzy Polynomial Approximation with Triangular Linear Diophantine Least Squares

Modeling uncertainty and imprecision is a substantial challenge in a variety of scientific and engineering domains. Conventional techniques, such as intuitionistic, Pythagorean, and q-rung orthopair fuzzy sets, have a restricted ability to capture all degrees of membership and non-membership. This study introduces a triangular linear Diophantine fuzzy least squares polynomial, which provides an efficient and reliable framework for evaluating fuzzy problems. Numerical test problems from engineering are utilized to demonstrate the applicability and precision of the method compared to existing schemes. The numerical results reveal that the developed technique is more reliable and efficient than the existing methods in terms of memory usage, memory utilization, mean square error, root square error, standard deviations, and time to find the approximate solution to the fuzzy problem. The numerical findings show that the proposed triangular linear Diophantine fuzzy least-square framework is the best alternative to address scientific and technical problems.