Necessary and sufficient conditions for interval-valued differentiability

被引：6

作者：

Osuna-Gomez, Rafaela ^{[1
]}

Mendonca da Costa, Tiago ^{[2
]}

Hernandez-Jimenez, Beatriz ^{[3
]}

Ruiz-Garzon, Gabriel ^{[4
]}

机构：

[1] Univ Seville, Dept Estadist & Invest Operat, Seville, Spain

[2] Univ Tarapaca, Dept Matemat, Casilla 7D, Arica, Chile

[3] Univ Pablo de Olavide, Dept Econ M Cuantitat & H Econ, Seville, Spain

[4] Univ Cadiz, Dept Estadist & IO, Campus Jerez, Jerez de la Frontera, Spain

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2023年 / 46卷 / 02期

关键词：

generalized Hukuhara differentiability; interval analysis; interval-valued functions; OPTIMIZATION PROBLEMS; EQUATIONS; EXISTENCE; CALCULUS;

D O I：

10.1002/mma.8647

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents necessary and sufficient conditions for generalized Hukuhara differentiability of interval-valued functions and counterexamples of some equivalences previously presented in the literature, for which important results are based on. Moreover, applications of interval generalized Hukuhara differentiability are presented.

引用

页码：2319 / 2333

页数：15

共 26 条

[1]

Aubin J.-P., 2012, Differential inclusions: set-valued maps and viability theory, V264

[2] Generalized differentiability of fuzzy-valued functions [J].

Bede, Barnabas ;

Stefanini, Luciano .

FUZZY SETS AND SYSTEMS, 2013, 230 :119-141

[3] Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative [J].

Chalco-Cano, Y. ;

Lodwick, W. A. ;

Rufian-Lizana, A. .

FUZZY OPTIMIZATION AND DECISION MAKING, 2013, 12 (03) :305-322

[4] Calculus for interval-valued functions using generalized Hukuhara derivative and applications [J].

Chalco-Cano, Y. ;

Rufian-Lizana, A. ;

Roman-Flores, H. ;

Jimenez-Gamero, M. D. .

FUZZY SETS AND SYSTEMS, 2013, 219 :49-67

[5]

Chalco-Cano Y, 2012, COMPUT APPL MATH, V31, P457

[6] Gauss-type integral inequalities for interval and fuzzy-interval-valued functions [J].

Costa, T. M. ;

Silva, G. N. ;

Chalco-Cano, Y. ;

Roman-Flores, H. .

COMPUTATIONAL & APPLIED MATHEMATICS, 2019, 38 (02)

[7]

Diamond P., 1994, Metric Space of Fuzzy Sets

[8]

Ghosh D., 2021, GEN HUKUHARA GRADIEN, P1275, DOI [10.1007/s40815-021-01175-x, DOI 10.1007/S40815]

[9] Generalized Hukuhara Gateaux and Frechet derivatives of interval-valued functions and their application in optimization with interval-valued functions [J].

Ghosh, Debdas ;

Chauhan, Ram Surat ;

Mesiar, Radko ;

Debnath, Amit Kumar .

INFORMATION SCIENCES, 2020, 510 :317-340

[10] Extended Karush-Kuhn-Tucker condition for constrained interval optimization problems and its application in support vector machines [J].

Ghosh, Debdas ;

Singh, Abhishek ;

Shukla, K. K. ;

Manchanda, Kartik .

INFORMATION SCIENCES, 2019, 504 :276-292

← 1 2 3 →