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The Fuzzy Riemann-Stieltjes Integral
被引:8
作者
:
Ren, Xuekun
论文数:
0
引用数:
0
h-index:
0
机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Ren, Xuekun
[
1
]
Wu, Chong
论文数:
0
引用数:
0
h-index:
0
机构:
Harbin Inst Technol, Sch Management, Harbin 150001, Peoples R China
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Wu, Chong
[
2
]
机构
:
[1]
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
[2]
Harbin Inst Technol, Sch Management, Harbin 150001, Peoples R China
来源
:
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
|
2013年
/ 52卷
/ 06期
关键词
:
Fuzzy-number-valued functions;
Fuzzy integral;
Fuzzy Riemann-Stieltjes integral;
DIFFERENTIAL-CALCULUS;
EQUATION;
D O I
:
10.1007/s10773-013-1511-9
中图分类号
:
O4 [物理学];
学科分类号
:
0702 ;
摘要
:
In this paper, we define fuzzy Riemann-Stieltjes integral of fuzzy-number-valued functions directly; discuss properties of the integral and present several necessary and sufficient conditions of integrability for fuzzy-number-valued function.
引用
收藏
页码:2134 / 2151
页数:18
相关论文
共 16 条
[1]
[Anonymous], 1988, Possibility Theory
[2]
Nodal solutions of boundary value problems with boundary conditions involving Riemann-Stieltjes integrals
Chamberlain, Jeremy
论文数:
0
引用数:
0
h-index:
0
机构:
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
Chamberlain, Jeremy
Kong, Lingju
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Tennessee, Dept Math, Chattanooga, TN 37403 USA
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
Kong, Lingju
Kong, Qingkai
论文数:
0
引用数:
0
h-index:
0
机构:
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
Kong, Qingkai
[J].
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,
2011,
74
(06)
: 2380
-
2387
[3]
Approximating the Riemann-Stieltjes integral by a trapezoidal quadrature rule with applications
Dragomir, S. S.
论文数:
0
引用数:
0
h-index:
0
机构:
Victoria Univ, Sch Sci & Engn, Melbourne, MC 8001, Australia
Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
Victoria Univ, Sch Sci & Engn, Melbourne, MC 8001, Australia
Dragomir, S. S.
[J].
MATHEMATICAL AND COMPUTER MODELLING,
2011,
54
(1-2)
: 243
-
260
[4]
TOWARDS FUZZY DIFFERENTIAL-CALCULUS .2. INTEGRATION ON FUZZY INTERVALS
DUBOIS, D
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
DUBOIS, D
PRADE, H
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
PRADE, H
[J].
FUZZY SETS AND SYSTEMS,
1982,
8
(02)
: 105
-
116
[5]
TOWARDS FUZZY DIFFERENTIAL-CALCULUS .1. INTEGRATION OF FUZZY MAPPINGS
DUBOIS, D
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3, F-31062 TOULOUSE, FRANCE
UNIV TOULOUSE 3, F-31062 TOULOUSE, FRANCE
DUBOIS, D
PRADE, H
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3, F-31062 TOULOUSE, FRANCE
UNIV TOULOUSE 3, F-31062 TOULOUSE, FRANCE
PRADE, H
[J].
FUZZY SETS AND SYSTEMS,
1982,
8
(01)
: 1
-
17
[6]
TOWARDS FUZZY DIFFERENTIAL-CALCULUS .3. DIFFERENTIATION
DUBOIS, D
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
DUBOIS, D
PRADE, H
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
PRADE, H
[J].
FUZZY SETS AND SYSTEMS,
1982,
8
(03)
: 225
-
233
[7]
Bounded variation, absolute continuity and absolute integrability for fuzzy-number-valued functions
Gong, ZT
论文数:
0
引用数:
0
h-index:
0
机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Gong, ZT
Wu, CX
论文数:
0
引用数:
0
h-index:
0
机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Wu, CX
[J].
FUZZY SETS AND SYSTEMS,
2002,
129
(01)
: 83
-
94
[8]
Kelley J. L., 1955, General Topology
[9]
Properties of the boundary integral equation for solar non-constant-α force-free magnetic fields
Li, ZH
论文数:
0
引用数:
0
h-index:
0
机构:
Chinese Acad Sci, Natl Astron Observ, Beijing 100012, Peoples R China
Chinese Acad Sci, Natl Astron Observ, Beijing 100012, Peoples R China
Li, ZH
Yan, YH
论文数:
0
引用数:
0
h-index:
0
机构:
Chinese Acad Sci, Natl Astron Observ, Beijing 100012, Peoples R China
Yan, YH
Song, GX
论文数:
0
引用数:
0
h-index:
0
机构:
Chinese Acad Sci, Natl Astron Observ, Beijing 100012, Peoples R China
Song, GX
[J].
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,
2004,
347
(04)
: 1255
-
1265
[10]
ON INTEGRATION OF FUZZY MAPPINGS
NANDA, S
论文数:
0
引用数:
0
h-index:
0
NANDA, S
[J].
FUZZY SETS AND SYSTEMS,
1989,
32
(01)
: 95
-
101
←
1
2
→
共 16 条
[1]
[Anonymous], 1988, Possibility Theory
[2]
Nodal solutions of boundary value problems with boundary conditions involving Riemann-Stieltjes integrals
Chamberlain, Jeremy
论文数:
0
引用数:
0
h-index:
0
机构:
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
Chamberlain, Jeremy
Kong, Lingju
论文数:
0
引用数:
0
h-index:
0
机构:
Univ Tennessee, Dept Math, Chattanooga, TN 37403 USA
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
Kong, Lingju
Kong, Qingkai
论文数:
0
引用数:
0
h-index:
0
机构:
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
No Illinois Univ, Dept Math, De Kalb, IL 60115 USA
Kong, Qingkai
[J].
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,
2011,
74
(06)
: 2380
-
2387
[3]
Approximating the Riemann-Stieltjes integral by a trapezoidal quadrature rule with applications
Dragomir, S. S.
论文数:
0
引用数:
0
h-index:
0
机构:
Victoria Univ, Sch Sci & Engn, Melbourne, MC 8001, Australia
Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa
Victoria Univ, Sch Sci & Engn, Melbourne, MC 8001, Australia
Dragomir, S. S.
[J].
MATHEMATICAL AND COMPUTER MODELLING,
2011,
54
(1-2)
: 243
-
260
[4]
TOWARDS FUZZY DIFFERENTIAL-CALCULUS .2. INTEGRATION ON FUZZY INTERVALS
DUBOIS, D
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
DUBOIS, D
PRADE, H
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
PRADE, H
[J].
FUZZY SETS AND SYSTEMS,
1982,
8
(02)
: 105
-
116
[5]
TOWARDS FUZZY DIFFERENTIAL-CALCULUS .1. INTEGRATION OF FUZZY MAPPINGS
DUBOIS, D
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3, F-31062 TOULOUSE, FRANCE
UNIV TOULOUSE 3, F-31062 TOULOUSE, FRANCE
DUBOIS, D
PRADE, H
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3, F-31062 TOULOUSE, FRANCE
UNIV TOULOUSE 3, F-31062 TOULOUSE, FRANCE
PRADE, H
[J].
FUZZY SETS AND SYSTEMS,
1982,
8
(01)
: 1
-
17
[6]
TOWARDS FUZZY DIFFERENTIAL-CALCULUS .3. DIFFERENTIATION
DUBOIS, D
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
DUBOIS, D
PRADE, H
论文数:
0
引用数:
0
h-index:
0
机构:
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
UNIV TOULOUSE 3,F-31062 TOULOUSE,FRANCE
PRADE, H
[J].
FUZZY SETS AND SYSTEMS,
1982,
8
(03)
: 225
-
233
[7]
Bounded variation, absolute continuity and absolute integrability for fuzzy-number-valued functions
Gong, ZT
论文数:
0
引用数:
0
h-index:
0
机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Gong, ZT
Wu, CX
论文数:
0
引用数:
0
h-index:
0
机构:
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China
Wu, CX
[J].
FUZZY SETS AND SYSTEMS,
2002,
129
(01)
: 83
-
94
[8]
Kelley J. L., 1955, General Topology
[9]
Properties of the boundary integral equation for solar non-constant-α force-free magnetic fields
Li, ZH
论文数:
0
引用数:
0
h-index:
0
机构:
Chinese Acad Sci, Natl Astron Observ, Beijing 100012, Peoples R China
Chinese Acad Sci, Natl Astron Observ, Beijing 100012, Peoples R China
Li, ZH
Yan, YH
论文数:
0
引用数:
0
h-index:
0
机构:
Chinese Acad Sci, Natl Astron Observ, Beijing 100012, Peoples R China
Yan, YH
Song, GX
论文数:
0
引用数:
0
h-index:
0
机构:
Chinese Acad Sci, Natl Astron Observ, Beijing 100012, Peoples R China
Song, GX
[J].
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,
2004,
347
(04)
: 1255
-
1265
[10]
ON INTEGRATION OF FUZZY MAPPINGS
NANDA, S
论文数:
0
引用数:
0
h-index:
0
NANDA, S
[J].
FUZZY SETS AND SYSTEMS,
1989,
32
(01)
: 95
-
101
←
1
2
→