Advanced fuzzy polynomial approximation with triangular linear diophantine least squares

Abstract

Modeling uncertainty and imprecision is a substantial challenge in a variety of scientific and engineeringdomains. Conventional techniques, such as intuitionistic, Pythagorean, andq-rung orthopair fuzzy sets, have a restrictedability to capture all degrees of membership and non-membership. This study introduces a triangular linear Diophantinefuzzy 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 methodcompared to existing schemes. The numerical results reveal that the developed technique is more reliable and efficientthan the existing methods in terms of memory usage, memory utilization, mean square error, root square error, standarddeviations,andtimetofindtheapproximatesolutiontothefuzzyproblem. Thenumericalfindingsshowthattheproposedtriangular linear Diophantine fuzzy least-square framework is the best alternative to address scientific and technicalproblems