On Approximation by Truncated Max-Product Baskakov Operators of Fuzzy Numbers

Abstract

In this work, the truncated max-product (non-linear) Baskakov operators were generalized to encompass any compact interval [a, b], as it was proven that they had the same order of uniform approximation as in the specific case of the interval [0, 1]. Furthermore, it was proven that the monotonicity and shape properties were preserved by these operators on [a, b]. Moreover, for applications, a fuzzy number R^M(p,[a,b])(t) was generated, preserving the support and the core of an arbitrary ρ, and they were utilized through metrics D_C and L^1−type metrics to improve convergence estimates. Several direct conclusions were also obtained. Finally, a comparison and an illustrative graphic were presented, demonstrating how these operators converged to a fuzzy function