• 论文 •

### 基于$K$-拟算术运算诱导的$Kp$-积分模意义下分片线性函数的逼近

1. 1.通化师范学院数学学院, 通化 134002;2.天津师范大学数学科学学院,天津 300387
• 出版日期:2016-02-25 发布日期:2016-03-10

TAO Yujie,WANG Hongzhi,WANG Guijun. APPROXIMATION OF PIECEWISE LINEAR FUNCTION IN THE SENSE OF $Kp$-INTEGRAL NORM INDUCED BY $K$-QUASI-ARITHMETIC OPERATIONS[J]. Journal of Systems Science and Mathematical Sciences, 2016, 36(2): 267-.

### APPROXIMATION OF PIECEWISE LINEAR FUNCTION IN THE SENSE OF $Kp$-INTEGRAL NORM INDUCED BY $K$-QUASI-ARITHMETIC OPERATIONS

TAO Yujie 1,WANG Hongzhi1 ,WANG Guijun2

1. 1.School of Mathematics, Tonghua Normal University, Tonghua 134002; 2.School of Mathematics Sciences, Tianjin Normal University, Tianjin 300387
• Online:2016-02-25 Published:2016-03-10

Integral norm is a metric to describe a class of integrable function space, piecewise linear function is a bridge to connect relationship between fuzzy system and approximation function. They are two important tools to study the approximation problem of generalized fuzzy system. Firstly, the $Kp$-integral norm is defined by extending the quasi-subtraction operator, and we proved that the $Kp$-integral norm is a metric about quasi-addition operator by the integral transformation theorem. Secondly, it is obtained that the piecewise linear functions can approximate a kind of $\hat{\mu}_{p}$-integrable functions to arbitrary accuracy with respect to the $Kp$-integral norm.

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