Fuzzy Cubic Spline Interpolation And Fuzzy Least Squares Approximation

It often need to statistics and analysis many datas in production practice,sometimes these properties can solve by the help of fuzzy number and processing because of many measures or experimental data in equipments and technology are uncertain.As a result,the numerical approximation based on the uncertainty of fuzzy number has attracted more and more attention from scholars in the field of fuzzy mathematics in recent yearsIn this paper,we use the classical cubic spline interpolation and least squares approximation method to discuss the problem about fuzzy cubic spline interpolation and fuzzy least squares approximation problems based on LR fuzzy number.we propose and construct two kinds of specific expressions of approximation function,respectively.And prove that the existence and uniqueness theorem of the fuzzy interpolation polynomial and fuzzy least squares approximation,meanwhile,gave the corresponding remainder term expression and error analysis.First of all,this part propose the basic concepts such as fuzzy sets and LR fuzzy numbers.Secondly,define the LR fuzzy polynomial and LR fuzzy interpolation polynomial,and construct a specific formula of LR fuzzy cubic spline interpolation method.Thirdly,discuss fuzzy least squares approximation based on LR fuzzy number.Finally,several numerical examples are given to illustrate the constructed interpolation method and the validity of the numerical approximation method in this paper.