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Volumn 219, Issue , 2013, Pages 49-67

Calculus for interval-valued functions using generalized Hukuhara derivative and applications

Author keywords

Differentiability; Fuzzy functions; Generalized Hukuhara difference; Integrability; Interval valued functions

Indexed keywords

DIFFERENTIABILITY; FUZZY FUNCTION; GENERALIZED HUKUHARA DIFFERENCES; INTEGRABILITY; INTERVAL-VALUED FUNCTION;

EID: 84875221180     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2012.12.004     Document Type: Article
Times cited : (180)

References (57)
  • 1
    • 67349149220 scopus 로고    scopus 로고
    • Existence for set differential equations via multivalued operator equations
    • Nova Science Publishers, New York
    • R.P. Agarwal, D. O'Regan, Existence for set differential equations via multivalued operator equations, in: Differential Equations and Applications, vol. 5, Nova Science Publishers, New York, 2007, pp. 1-5.
    • (2007) Differential Equations and Applications , vol.5 , pp. 1-5
    • Agarwal, R.P.1    O'Regan, D.2
  • 4
    • 77956609472 scopus 로고    scopus 로고
    • Introduction set-valued analysis in control theory
    • J.P. Aubin, and H. Franskowska Introduction set-valued analysis in control theory Set-Valued Anal. 8 2000 1 9
    • (2000) Set-Valued Anal. , vol.8 , pp. 1-9
    • Aubin, J.P.1    Franskowska, H.2
  • 5
    • 17444409461 scopus 로고
    • Quasilinear operators and their application in the theory of multivalued mappings
    • S.M. Assev, Quasilinear operators and their application in the theory of multivalued mappings, in: Proceedings of the Steklov Institute of Mathematics, vol. 2, 1986, pp. 23-52.
    • (1986) Proceedings of the Steklov Institute of Mathematics , vol.2 , pp. 23-52
    • Assev, S.M.1
  • 6
    • 0014742116 scopus 로고
    • A differential calculus for multifunctions
    • H.T. Banks, and M.Q. Jacobs A differential calculus for multifunctions J. Math. Anal. Appl. 29 1970 246 272
    • (1970) J. Math. Anal. Appl. , vol.29 , pp. 246-272
    • Banks, H.T.1    Jacobs, M.Q.2
  • 7
    • 14544296605 scopus 로고    scopus 로고
    • Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equation
    • B. Bede, and S.G. Gal Generalizations of the differentiability of fuzzy number valued functions with applications to fuzzy differential equation Fuzzy Sets Syst. 151 2005 581 599
    • (2005) Fuzzy Sets Syst. , vol.151 , pp. 581-599
    • Bede, B.1    Gal, S.G.2
  • 8
    • 33846224330 scopus 로고    scopus 로고
    • First order linear fuzzy differential equations under generalized differentiability
    • B. Bede, I.J. Rudas, and A.L. Bencsik First order linear fuzzy differential equations under generalized differentiability Inf. Sci. 177 2007 1648 1662
    • (2007) Inf. Sci. , vol.177 , pp. 1648-1662
    • Bede, B.1    Rudas, I.J.2    Bencsik, A.L.3
  • 9
    • 77958163688 scopus 로고    scopus 로고
    • Solutions of fuzzy differential equations based on generalized differentiability
    • B. Bede, and S.G. Gal Solutions of fuzzy differential equations based on generalized differentiability Commun. Math. Anal. 9 2010 22 41
    • (2010) Commun. Math. Anal. , vol.9 , pp. 22-41
    • Bede, B.1    Gal, S.G.2
  • 10
    • 0001530156 scopus 로고
    • Linear multiple objective problems with interval coefficients
    • G.R. Bitran Linear multiple objective problems with interval coefficients Manage. Sci. 26 1980 694 706
    • (1980) Manage. Sci. , vol.26 , pp. 694-706
    • Bitran, G.R.1
  • 11
    • 0002555470 scopus 로고
    • On the differentiability of multifunctions
    • F.S. De Blasi On the differentiability of multifunctions Pac. J. Math. 66 1976 67 81
    • (1976) Pac. J. Math. , vol.66 , pp. 67-81
    • De Blasi, F.S.1
  • 12
    • 35348968006 scopus 로고    scopus 로고
    • An existence theorem for set differential inclusions in a semilinear metric space
    • F.S. De Blasi, V. Lakshmikantham, and T.G. Bhaskar An existence theorem for set differential inclusions in a semilinear metric space Control Cybern. 36 3 2007 571 582
    • (2007) Control Cybern. , vol.36 , Issue.3 , pp. 571-582
    • De Blasi, F.S.1    Lakshmikantham, V.2    Bhaskar, T.G.3
  • 13
    • 79953282911 scopus 로고    scopus 로고
    • Generalized derivative and π-derivative for set-valued functions
    • Y. Chalco-Cano, H. Román-Flores, and M.D. Jiménez-Gamero Generalized derivative and π-derivative for set-valued functions Inf. Sci. 181 2011 2177 2188
    • (2011) Inf. Sci. , vol.181 , pp. 2177-2188
    • Chalco-Cano, Y.1    Román-Flores, H.2    Jiménez-Gamero, M.D.3
  • 16
    • 64049113935 scopus 로고    scopus 로고
    • Comparison between some approaches to solve fuzzy differential equations
    • Y. Chalco-Cano, and H. Román-Flores Comparison between some approaches to solve fuzzy differential equations Fuzzy Sets Syst. 160 2009 1517 1527
    • (2009) Fuzzy Sets Syst. , vol.160 , pp. 1517-1527
    • Chalco-Cano, Y.1    Román-Flores, H.2
  • 19
    • 0030575675 scopus 로고    scopus 로고
    • Multiobjective programming in optimization of interval objective functions - A generalized approach
    • S. Chanas, and D. Kuchta Multiobjective programming in optimization of interval objective functions - a generalized approach Eur. J. Oper. Res. 94 1996 594 598
    • (1996) Eur. J. Oper. Res. , vol.94 , pp. 594-598
    • Chanas, S.1    Kuchta, D.2
  • 20
    • 0345633659 scopus 로고    scopus 로고
    • Multiobjective transportation problem with interval cost, source and destination parameters
    • S.K. Das, A. Goswami, and S.S. Alam Multiobjective transportation problem with interval cost, source and destination parameters Eur. J. Oper. Res. 17 1999 100 112
    • (1999) Eur. J. Oper. Res. , vol.17 , pp. 100-112
    • Das, S.K.1    Goswami, A.2    Alam, S.S.3
  • 22
    • 14644437111 scopus 로고    scopus 로고
    • Set valued functions in Fréchet spaces continuity, Hukuhara differentiability and applications to set differential equations
    • G.N. Galanis, T. Gnana Bhaskar, V. Lakshmikantham, and P.K. Palamides Set valued functions in Fréchet spaces continuity, Hukuhara differentiability and applications to set differential equations Nonlinear Anal. Theory Methods Appl. 61 2005 559 575
    • (2005) Nonlinear Anal. Theory Methods Appl. , vol.61 , pp. 559-575
    • Galanis, G.N.1    Gnana Bhaskar, T.2    Lakshmikantham, V.3    Palamides, P.K.4
  • 24
    • 0042412264 scopus 로고    scopus 로고
    • Set differential equations and flow invariance
    • T. Gnana Bhaskar, and V. Lakshmikantham Set differential equations and flow invariance Applicable Anal. 82 2003 357 368
    • (2003) Applicable Anal. , vol.82 , pp. 357-368
    • Gnana Bhaskar, T.1    Lakshmikantham, V.2
  • 26
    • 0042121384 scopus 로고    scopus 로고
    • Impulsive functional differential inclusions and fuzzy population models
    • M. Guo, X. Xue, and R. Li Impulsive functional differential inclusions and fuzzy population models Fuzzy Sets Syst. 138 2003 601 615
    • (2003) Fuzzy Sets Syst. , vol.138 , pp. 601-615
    • Guo, M.1    Xue, X.2    Li, R.3
  • 27
    • 0012777173 scopus 로고
    • Integration des applications mesurables dont la valeur est un compact convexe
    • M. Hukuhara Integration des applications mesurables dont la valeur est un compact convexe Funkcial. Ekvac. 10 1967 205 223
    • (1967) Funkcial. Ekvac. , vol.10 , pp. 205-223
    • Hukuhara, M.1
  • 28
    • 0009782615 scopus 로고    scopus 로고
    • On the differentiability of set-valued functions defined on a Banach space and mean value theorem
    • A-G.M. Ibrahim On the differentiability of set-valued functions defined on a Banach space and mean value theorem Appl. Math. Comput. 74 1996 76 94
    • (1996) Appl. Math. Comput. , vol.74 , pp. 76-94
    • Ibrahim, A.-G.M.1
  • 29
    • 0026171352 scopus 로고
    • Goal programming problems with interval coefficients and target intervals
    • M. Inuiguchi, and Y. Kume Goal programming problems with interval coefficients and target intervals Eur. J. Oper. Res. 52 1991 345 360
    • (1991) Eur. J. Oper. Res. , vol.52 , pp. 345-360
    • Inuiguchi, M.1    Kume, Y.2
  • 30
    • 0040973455 scopus 로고
    • Minimax regret solution to linear programming problems with an interval objective function
    • M. Inuiguchi, and M. Sakawa Minimax regret solution to linear programming problems with an interval objective function Eur. J. Oper. Res. 86 1995 526 536
    • (1995) Eur. J. Oper. Res. , vol.86 , pp. 526-536
    • Inuiguchi, M.1    Sakawa, M.2
  • 31
    • 0001862777 scopus 로고    scopus 로고
    • Possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem
    • M. Inuiguchi, and J. Ramík Possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem Fuzzy Sets Syst. 111 2000 3 28
    • (2000) Fuzzy Sets Syst. , vol.111 , pp. 3-28
    • Inuiguchi, M.1    Ramík, J.2
  • 32
    • 0025480980 scopus 로고
    • Multiobjective programming in optimization of the interval objective function
    • H. Ishibushi, and H. Tanaka Multiobjective programming in optimization of the interval objective function Eur. J. Oper. Res. 48 1990 219 225
    • (1990) Eur. J. Oper. Res. , vol.48 , pp. 219-225
    • Ishibushi, H.1    Tanaka, H.2
  • 33
    • 3042760657 scopus 로고
    • Discrimination methods of efficient solutions for multiobjective linear programming problems with interval coefficients
    • M. Ida, and O. Katai Discrimination methods of efficient solutions for multiobjective linear programming problems with interval coefficients Trans. SICE 29 1993 1247 1249
    • (1993) Trans. SICE , vol.29 , pp. 1247-1249
    • Ida, M.1    Katai, O.2
  • 34
    • 0030388505 scopus 로고    scopus 로고
    • Multiple objective linear programming with interval coefficients and its all efficient solutions
    • Kobe
    • M. Ida, Multiple objective linear programming with interval coefficients and its all efficient solutions, in: Proceedings of IEEE CDC, Kobe, 1996, pp. 1247-1249.
    • (1996) Proceedings of IEEE CDC , pp. 1247-1249
    • Ida, M.1
  • 35
    • 37449003041 scopus 로고    scopus 로고
    • A nonlinear interval number programming method for uncertain optimization problems
    • C. Jiang, X. Han, G.R. Liu, and G.P. Liu A nonlinear interval number programming method for uncertain optimization problems Eur. J. Oper. Res. 188 2008 1 13
    • (2008) Eur. J. Oper. Res. , vol.188 , pp. 1-13
    • Jiang, C.1    Han, X.2    Liu, G.R.3    Liu, G.P.4
  • 36
    • 30144435903 scopus 로고    scopus 로고
    • A note on fuzzy differential equations
    • O. Kaleva A note on fuzzy differential equations Nonlinear Anal. 64 2006 895 900
    • (2006) Nonlinear Anal. , vol.64 , pp. 895-900
    • Kaleva, O.1
  • 37
    • 0032127713 scopus 로고    scopus 로고
    • A non-stochastic approach for modelling uncertainty in population dynamics
    • V. Krivan, and G. Colombo A non-stochastic approach for modelling uncertainty in population dynamics Bull. Math. Biol. 60 1998 721 751
    • (1998) Bull. Math. Biol. , vol.60 , pp. 721-751
    • Krivan, V.1    Colombo, G.2
  • 38
    • 0041387380 scopus 로고    scopus 로고
    • Existence and interrelation between set and fuzzy differential equations
    • V. Lakshmikantham, and A.A. Tolstonogov Existence and interrelation between set and fuzzy differential equations Nonlinear Anal. 55 3 2003 255 268
    • (2003) Nonlinear Anal. , vol.55 , Issue.3 , pp. 255-268
    • Lakshmikantham, V.1    Tolstonogov, A.A.2
  • 41
    • 2342637233 scopus 로고
    • Calculus for interval functions of a real variable
    • S. Markov Calculus for interval functions of a real variable Computing 22 1979 325 337
    • (1979) Computing , vol.22 , pp. 325-337
    • Markov, S.1
  • 42
    • 0004293209 scopus 로고
    • Prentice-Hall Englewood Cliffs, NJ
    • R.E. Moore Interval Analysis 1966 Prentice-Hall Englewood Cliffs, NJ
    • (1966) Interval Analysis
    • Moore, R.E.1
  • 44
    • 67349278129 scopus 로고    scopus 로고
    • Stability of set differential equations and applications
    • Nguyen Ngoc Tu, and Tran Thanh Tung Stability of set differential equations and applications Nonlinear Anal. Theory, Methods Appl. 71 2009 1526 1533
    • (2009) Nonlinear Anal. Theory, Methods Appl. , vol.71 , pp. 1526-1533
    • Tu, N.N.1    Tung, T.T.2
  • 45
    • 0009756910 scopus 로고    scopus 로고
    • The Cauchy problem of continuous fuzzy differential equations
    • J.J. Nieto The Cauchy problem of continuous fuzzy differential equations Fuzzy Set Syst. 102 1999 259 262
    • (1999) Fuzzy Set Syst. , vol.102 , pp. 259-262
    • Nieto, J.J.1
  • 46
    • 33947677215 scopus 로고    scopus 로고
    • Multiple objective linear programming models with interval coefficients - An illustrated overview
    • C. Oliveira, and C. Henggeler Antunes Multiple objective linear programming models with interval coefficients - an illustrated overview Eur. J. Oper. Res. 181 2007 1434 1463
    • (2007) Eur. J. Oper. Res. , vol.181 , pp. 1434-1463
    • Oliveira, C.1    Henggeler Antunes, C.2
  • 47
    • 84974069723 scopus 로고
    • Limit theorem for random compact sets in Banach spaces
    • M. Puri, and D. Ralescu Limit theorem for random compact sets in Banach spaces Math. Proc. Cambridge Philos. Soc. 97 1985 151 158
    • (1985) Math. Proc. Cambridge Philos. Soc. , vol.97 , pp. 151-158
    • Puri, M.1    Ralescu, D.2
  • 48
    • 0036646539 scopus 로고    scopus 로고
    • Embedding of level-continuous fuzzy sets on Banach spaces
    • H. Román-Flores, and M. Rojas-Medar Embedding of level-continuous fuzzy sets on Banach spaces Inf. Sci. 144 2002 227 247
    • (2002) Inf. Sci. , vol.144 , pp. 227-247
    • Román-Flores, H.1    Rojas-Medar, M.2
  • 49
    • 67349163185 scopus 로고    scopus 로고
    • Generalized Hukuhara differentiability of interval-valued functions and interval differential equations
    • L. Stefanini, and B. Bede Generalized Hukuhara differentiability of interval-valued functions and interval differential equations Nonlinear Anal. 71 2009 1311 1328
    • (2009) Nonlinear Anal. , vol.71 , pp. 1311-1328
    • Stefanini, L.1    Bede, B.2
  • 51
    • 77949914993 scopus 로고    scopus 로고
    • A generalization of Hukuhara difference and division for interval and fuzzy arithmetic
    • L. Stefanini A generalization of Hukuhara difference and division for interval and fuzzy arithmetic Fuzzy Sets Syst. 161 2010 1564 1584
    • (2010) Fuzzy Sets Syst. , vol.161 , pp. 1564-1584
    • Stefanini, L.1
  • 52
    • 0013409929 scopus 로고
    • Fixed points, fixed sets, and m-retracts
    • W. Strother Fixed points, fixed sets, and m-retracts Duke Math. J. 22 1955 551 556
    • (1955) Duke Math. J. , vol.22 , pp. 551-556
    • Strother, W.1
  • 53
    • 0013409930 scopus 로고
    • Continuous multi-valued functions
    • W. Strother Continuous multi-valued functions Bol. Soc. Mat. São Paulo 10 1958 87 120
    • (1958) Bol. Soc. Mat. São Paulo , vol.10 , pp. 87-120
    • Strother, W.1
  • 54
    • 0005516533 scopus 로고
    • An application of the central limit theorem for Banach-space valued random variables to the theory of random sets
    • W. Weil An application of the central limit theorem for Banach-space valued random variables to the theory of random sets Z. Wahrscheinlichkeitstheorie Geb. 60 1982 203 208
    • (1982) Z. Wahrscheinlichkeitstheorie Geb. , vol.60 , pp. 203-208
    • Weil, W.1
  • 55
    • 33748980066 scopus 로고    scopus 로고
    • The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function
    • H.-C. Wu The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective function Eur. J. Oper. Res. 176 2007 46 59
    • (2007) Eur. J. Oper. Res. , vol.176 , pp. 46-59
    • Wu, H.-C.1
  • 56
    • 56549121917 scopus 로고    scopus 로고
    • The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions
    • H.-C. Wu The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions Eur. J. Oper. Res. 196 2009 49 60
    • (2009) Eur. J. Oper. Res. , vol.196 , pp. 49-60
    • Wu, H.-C.1
  • 57
    • 69549095843 scopus 로고    scopus 로고
    • The optimality conditions for optimization problems with convex constraints and multiple fuzzy-valued objective functions
    • H.-C. Wu The optimality conditions for optimization problems with convex constraints and multiple fuzzy-valued objective functions Fuzzy Optim. Decision Making 8 2009 295 321
    • (2009) Fuzzy Optim. Decision Making , vol.8 , pp. 295-321
    • Wu, H.-C.1


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