Abstract
In this paper, the fuzzy polynomial is introduced and applied to investigate the least squares approximation problem based on LR fuzzy numbers. A new and simple approach to solve the original problem is constructed by using approximate fuzzy polynomial. Two numerical examples are given to illustrate the proposed method. Since a large number of data exist as an uncertain property and need a function relation to reflect the laws between different variables, our results enrich fuzzy numerical approximation theory.
Highlights
Fuzzy Least Squares ApproximationErefore, p(x) (p(x), pl(x), pr(x)) is the solution of fuzzy least squares approximation
We investigated the fuzzy least squares approximation problem based on LR fuzzy numbers and proposed an approach to solve the fuzzy least squares approximation by using fuzzy polynomial approximation. e total deviation between the obtained approximation function and the known function is minimized
Numerical examples show that our method is feasible. is idea and method can be applied to the case in which the fitting function is of other types such as hyperbolic or exponential form
Summary
Erefore, p(x) (p(x), pl(x), pr(x)) is the solution of fuzzy least squares approximation. (nj a00a, ajφ1,j.(.x.), an), and is satisfied the with corresponding equation [11]; p(x) is the least squares solution of the data set (xi, f(xi)). Based on least squares solution, p(x) a0φ0(x)+ a1φ1(x) + · · · + anφn(x) is satisfied with equation [11]. An are the unique solution with equation [18] It proved that a unique function can be obtained p(x) a0φ0(x) + a1φ1(x) + · · · + anφn(x). wif xi − p xip xi − p∗ xi wif xi − p xi⎡⎢⎣aj − a∗j φj xi⎤⎥⎦. Erefore, p(x) is the least squares solution of data set (xi, f(xi))(i 1, 2, .
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