A New Definition of Fuzzy-Valued Function Limit(Continuity) and Its Derivability

殷凤; 王鹏飞

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A New Definition of Fuzzy-Valued Function Limit(Continuity) and Its Derivability

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- A New Definition of Fuzzy-Valued Function Limit(Continuity) and Its Derivability
- 模糊值函数极限(连续)及导数的新定义
- Vol. 32, Issue 6, Pages: 662-665(2011)
- 作者机构：
  
  忻州师范学院数学系
- 作者简介：
- 基金信息：
- DOI：
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- Published：2011
- 稿件说明：
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殷凤, 王鹏飞. A New Definition of Fuzzy-Valued Function Limit(Continuity) and Its Derivability[J]. 2011, 32(6): 662-665.
DOI：

殷凤, 王鹏飞. A New Definition of Fuzzy-Valued Function Limit(Continuity) and Its Derivability[J]. 2011, 32(6): 662-665. DOI：

摘要

介绍了模糊数的概念

模糊的运算规则

区间函数及模糊值函数的λ-截集

利用区间函数及模糊值函数的λ-截集给出模糊值函数的极限、连续和导数的定义.在此基础上首次提出模糊值函数一致极限、一致连续和一致导数的概念

并讨论了它们之间的关系.得出了模糊值函数在区间上有一致极限

则在区间上一致连续;在区间上一致连续

则在区间上有一致极限;在区间上一致可导

则在区间上一致连续的结论.

Abstract

The concept of fuzzy number

fuzzy arithmetic

interval function and λ-cut sets of fuzzy-valued functions were introduced.The definitions of limits

continuity and derivative of fuzzy-valued functions were given by using interval functions and λ-cut sets of fuzzy-valued function.Based on this agreement

the concepts of uniform limit

uniform continuity of fuzzy-valued functions and uniform derivatives were proposed and the relationship between them was discussed.It is concluded that: a fuzzy-valued function on the interval has the uniform limit

then it is uniform continuity in the same interval

it is uniformly continuity in the interval

it has uniform limit on the same interval too

and it is uniform derivability in the interval

it is uniformly continuity on the same interval.

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Keywords

references

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