结构元线性生成的模糊值函数的可导性
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摘要
用一种模糊距离给出结构元线性生成的模糊值函数极限的一种新定义,然后用这种极限给出结构元线性生成的模糊值函数导数的定义,并用该定义研究结构元线性生成的模糊值函数导数的加法、数乘运算、费马定理、罗尔定理、拉格朗日中值定理、极限定理、介值定理和极限的第一充分条件等基本性质.最后给出结构元线性生成的凸模糊值函数的定义,且探讨其性质.
We use a kind of fuzzy distance to give a new definition of the definite integral of fuzzy valued function for linear generation of structural elements. Then the definite integral definition is used to define the derivative of fuzzy valued function for linear generation of structural elements. By using this derivative definition,we study the properties of fuzzy valued function in the linear generation of structural elements. They are addition together with multiplication,Fermat theorem,Rolle theorem,Lagrange mean value theorem,limit theorem,intermediate value theorem,the nature of the first limit,and so on. Finally,the definition of convex fuzzy valued function for linear generation of structural elements is given,and its properties are discussed.
We use a kind of fuzzy distance to give a new definition of the definite integral of fuzzy valued function for linear generation of structural elements. Then the definite integral definition is used to define the derivative of fuzzy valued function for linear generation of structural elements. By using this derivative definition,we study the properties of fuzzy valued function in the linear generation of structural elements. They are addition together with multiplication,Fermat theorem,Rolle theorem,Lagrange mean value theorem,limit theorem,intermediate value theorem,the nature of the first limit,and so on. Finally,the definition of convex fuzzy valued function for linear generation of structural elements is given,and its properties are discussed.
引文
[1]巩增泰.模糊数值函数积分原函数的可导性问题[J].模糊系统与数学,2003,17(2):48-52.
[2]王鹏飞,殷凤,蔺小林.复模糊值函数的导数及其性质[J].黑龙江大学(自然科学学报),2009,26(4):486-489.
[3]张霞,徐义红.局部Lipschitz模糊函数的性质及广义方向导数[J].吉林大学学报(理学版),2015,53(5):873-876.
[4]PURI M L,RALESCU D. Differential for fuzzy fuction[J]. J Math Anal Appl,1983,91(2):552-558.
[5]GOETSCHEL R,VOXMAN W. Elementary fuzzy calculus[J]. Fuzzy Sets and Systems,1986,18(1):31-43.
[6]于兰芳,马树华,宋泽成,等.二元模糊值函数的导数和模糊波动方程[J].河北大学学报(自然科学版),2009,29(5):466-468.
[7]李法朝,仇计清,于向东,等. Fuzzy值函数的Fuzzy值导数[J].河北科技大学学报,1998,19(4):24-28.
[8]巩增泰,白玉娟.模糊有界变差函数全变差的积分表示与距离导数[J].数学学报,2011,54(4):633-642.
[9]王磊,郭嗣琮.线性生成的分数阶模糊微分方程[J].山东大学学报(理学版),2012,47(7):81-84.
[10]SEIKKALA S. On the fuzzy initial value problem[J]. Fuzzy Sets and Systems,1987,24(3):319-330.
[11]KANAGARAJAN K,SAMBATH M. Numerical solution of fuzzy differential equations by third order Runge-Kutta method[J].International J Applied Mathematics,2010,2(4):1-8.
[12]KALEVA O. Fuzzy differential equations[J]. Fuzzy Sets and Systens,1987,24(3):301-317.
[13]巩增泰.模糊数值函数积分原函数的可导性问题[J].兰州大学学报(自然科学版),2003,39(3):17-21.
[14]殷凤,王鹏飞.模糊值函数极限(连续)及导数的新定义[J].中北大学学报(自然科学版),2011,32(6):662-665.
[15]吴从炘,仇计清,李法朝,等.复Fuzzy函数的Buckley导数与Buckley积分[J].模糊系统与数学,1999,13(2):1-6.
[16]管斌.关于模糊数的若干结果[J].辽宁师范大学学报(自然科学版),1991,14(4):286-312.
[17]郭嗣琮.模糊值函数分析学的结构元方法(I)[J].辽宁工程技术大学学报,2002,21(5):670-674.
[18]李安国,金红伟,张志宏,等.模糊极限的一种新定义[J].辽宁工程技术大学学报,2004,23(6):845-847.
[19]郭嗣琮.模糊值函数分析学的结构元方法(II)[J].辽宁工程技术大学学报,2002,21(6):808-810.
[20]郭嗣琮.基于结构元理论的模糊数学分析原理[M].沈阳:东北大学出版社,2004:97-113.
[2]王鹏飞,殷凤,蔺小林.复模糊值函数的导数及其性质[J].黑龙江大学(自然科学学报),2009,26(4):486-489.
[3]张霞,徐义红.局部Lipschitz模糊函数的性质及广义方向导数[J].吉林大学学报(理学版),2015,53(5):873-876.
[4]PURI M L,RALESCU D. Differential for fuzzy fuction[J]. J Math Anal Appl,1983,91(2):552-558.
[5]GOETSCHEL R,VOXMAN W. Elementary fuzzy calculus[J]. Fuzzy Sets and Systems,1986,18(1):31-43.
[6]于兰芳,马树华,宋泽成,等.二元模糊值函数的导数和模糊波动方程[J].河北大学学报(自然科学版),2009,29(5):466-468.
[7]李法朝,仇计清,于向东,等. Fuzzy值函数的Fuzzy值导数[J].河北科技大学学报,1998,19(4):24-28.
[8]巩增泰,白玉娟.模糊有界变差函数全变差的积分表示与距离导数[J].数学学报,2011,54(4):633-642.
[9]王磊,郭嗣琮.线性生成的分数阶模糊微分方程[J].山东大学学报(理学版),2012,47(7):81-84.
[10]SEIKKALA S. On the fuzzy initial value problem[J]. Fuzzy Sets and Systems,1987,24(3):319-330.
[11]KANAGARAJAN K,SAMBATH M. Numerical solution of fuzzy differential equations by third order Runge-Kutta method[J].International J Applied Mathematics,2010,2(4):1-8.
[12]KALEVA O. Fuzzy differential equations[J]. Fuzzy Sets and Systens,1987,24(3):301-317.
[13]巩增泰.模糊数值函数积分原函数的可导性问题[J].兰州大学学报(自然科学版),2003,39(3):17-21.
[14]殷凤,王鹏飞.模糊值函数极限(连续)及导数的新定义[J].中北大学学报(自然科学版),2011,32(6):662-665.
[15]吴从炘,仇计清,李法朝,等.复Fuzzy函数的Buckley导数与Buckley积分[J].模糊系统与数学,1999,13(2):1-6.
[16]管斌.关于模糊数的若干结果[J].辽宁师范大学学报(自然科学版),1991,14(4):286-312.
[17]郭嗣琮.模糊值函数分析学的结构元方法(I)[J].辽宁工程技术大学学报,2002,21(5):670-674.
[18]李安国,金红伟,张志宏,等.模糊极限的一种新定义[J].辽宁工程技术大学学报,2004,23(6):845-847.
[19]郭嗣琮.模糊值函数分析学的结构元方法(II)[J].辽宁工程技术大学学报,2002,21(6):808-810.
[20]郭嗣琮.基于结构元理论的模糊数学分析原理[M].沈阳:东北大学出版社,2004:97-113.