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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

陶玉杰1,王宏志1,王贵君2   

  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

陶玉杰,王宏志,王贵君. 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[J]. 系统科学与数学, 2016, 36(2): 267-.

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

积分模是刻画一类可积函数空间的一个度量,分片线性函数是连通模糊系统和被逼近函数关系的桥梁, 二者是研究广义模糊系统逼近性问题的两个重要工具.首先通过拓广$K$-拟算术运算重新定义了$K_{p}$-积分模, 并依据积分转换定理证明该积分模关于拟加运算构成一个度量.其次,在$K_{p}$-积分模意义下获得了分片线性函数可按任意精度逼近一类$\hat{\mu}_{p}$-可积函数.

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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[1] 王宏志,陶玉杰,王贵君. 基于网格分片线性函数构造的非齐次线性 T-S模糊系统的逼近性分析[J]. 系统科学与数学, 2015, 35(11): 1276-1290.
[2] 彭维玲. 基于剖分模糊系统输入空间的多维分片线性函数的构造及逼近[J]. 系统科学与数学, 2014, 34(3): 340-351.
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