메뉴 건너뛰기




Volumn 13, Issue 2, 2012, Pages 860-881

Random fuzzy differential equations under generalized Lipschitz condition

Author keywords

Fuzziness and randomness in modelling; Fuzzy derivative; Fuzzy differential equation; Fuzzy random variable; Fuzzy stochastic process; Random fuzzy differential equation

Indexed keywords

FUZZINESS AND RANDOMNESS IN MODELLING; FUZZY DERIVATIVES; FUZZY DIFFERENTIAL EQUATIONS; FUZZY RANDOM VARIABLE; FUZZY STOCHASTIC PROCESS;

EID: 80054884842     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.08.022     Document Type: Article
Times cited : (84)

References (69)
  • 5
    • 0034599718 scopus 로고    scopus 로고
    • Fuzzy modelling in population dynamics
    • DOI 10.1016/S0304-3800(99)00223-9, PII S0304380099002239
    • L.C. Barros, R.C. Bassanezi, and P.A. Tonelli Fuzzy modelling in population dynamics Ecol. Model. 128 2000 27 33 (Pubitemid 30170351)
    • (2000) Ecological Modelling , vol.128 , Issue.1 , pp. 27-33
    • Barros, L.C.1    Bassanezi, R.C.2    Tonelli, P.A.3
  • 6
    • 80052025420 scopus 로고    scopus 로고
    • Fuzzy parameters in a partial differential equation model for population dispersal of leaf-cutting ants
    • 10.1016/j.nonrwa.2011.06.003
    • R. Motta Jafelice, C. Almeida, J.F.C.A. Meyer, and H.L. Vasconcelos Fuzzy parameters in a partial differential equation model for population dispersal of leaf-cutting ants Nonlinear Analysis RWA 2011 10.1016/j.nonrwa.2011.06.003
    • (2011) Nonlinear Analysis RWA
    • Motta Jafelice, R.1    Almeida, C.2    Meyer, J.F.C.A.3    Vasconcelos, H.L.4
  • 7
    • 77958041254 scopus 로고    scopus 로고
    • Fuzzy speed control and stability analysis of a networked induction motor system with time delays and packet dropouts
    • D. Zhao, C. Li, and J. Ren Fuzzy speed control and stability analysis of a networked induction motor system with time delays and packet dropouts Nonlinear Analysis RWA 12 2011 273 287
    • (2011) Nonlinear Analysis RWA , vol.12 , pp. 273-287
    • Zhao, D.1    Li, C.2    Ren, J.3
  • 8
    • 0023573517 scopus 로고
    • Fuzzy differential equations
    • O. Kaleva Fuzzy differential equations Fuzzy Sets and Systems 24 1987 301 317
    • (1987) Fuzzy Sets and Systems , vol.24 , pp. 301-317
    • Kaleva, O.1
  • 9
    • 0000363222 scopus 로고
    • The Cauchy problem for fuzzy differential equations
    • O. Kaleva The Cauchy problem for fuzzy differential equations Fuzzy Sets and Systems 35 1990 389 396
    • (1990) Fuzzy Sets and Systems , vol.35 , pp. 389-396
    • Kaleva, O.1
  • 11
    • 20444495547 scopus 로고    scopus 로고
    • Numerical Solution of Fuzzy Differential Equation by Runge-Kutta Method
    • S. Abbasbandy, and T. Allahviranloo Numerical solution of fuzzy differential equation by RungeKutta method Nonlinear Stud. 11 2004 117 129 (Pubitemid 38438757)
    • (2004) Nonlinear Stud. , vol.11 , Issue.1 , pp. 117-129
    • Abbasbandy, S.1    Viranloo, T.A.2
  • 12
    • 73249139676 scopus 로고    scopus 로고
    • On the concept of solution for fractional differential equations with uncertainty
    • R.P. Agarwal, V. Lakshmikantham, and J.J. Nieto On the concept of solution for fractional differential equations with uncertainty Nonlinear Anal. 72 2010 2859 2862
    • (2010) Nonlinear Anal. , vol.72 , pp. 2859-2862
    • Agarwal, R.P.1    Lakshmikantham, V.2    Nieto, J.J.3
  • 13
    • 0041387375 scopus 로고    scopus 로고
    • A stacking theorem approach for fuzzy differential equations
    • R.P. Agarwal, D. O'Regan, and V. Lakshmikantham A stacking theorem approach for fuzzy differential equations Nonlinear Anal. 55 2003 299 312
    • (2003) Nonlinear Anal. , vol.55 , pp. 299-312
    • Agarwal, R.P.1    O'Regan, D.2    Lakshmikantham, V.3
  • 14
    • 14544290543 scopus 로고    scopus 로고
    • Viability theory and fuzzy differential equations
    • DOI 10.1016/j.fss.2004.08.008, PII S0165011404003562
    • R.P. Agarwal, D. O'Regan, and V. Lakshmikantham Viability theory and fuzzy differential equations Fuzzy Sets and Systems 151 2005 563 580 (Pubitemid 40305078)
    • (2005) Fuzzy Sets and Systems , vol.151 , Issue.3 , pp. 563-580
    • Agarwal, R.P.1    O'Regan, D.2    Lakshmikantham, V.3
  • 15
    • 79955554059 scopus 로고    scopus 로고
    • On the fractional differential equations with uncertainty
    • S. Arshad, and V. Lupulescu On the fractional differential equations with uncertainty Nonlinear Anal. 74 2011 3685 3693
    • (2011) Nonlinear Anal. , vol.74 , pp. 3685-3693
    • Arshad, S.1    Lupulescu, V.2
  • 17
    • 14544296605 scopus 로고    scopus 로고
    • Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
    • DOI 10.1016/j.fss.2004.08.001, PII S0165011404003173
    • B. Bede, and S.G. Gal Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations Fuzzy Sets and Systems 151 2005 581 599 (Pubitemid 40305079)
    • (2005) Fuzzy Sets and Systems , vol.151 , Issue.3 , pp. 581-599
    • Bede, B.1    Gal, S.G.2
  • 18
    • 37349113426 scopus 로고    scopus 로고
    • Fuzzy solutions for impulsive differential equations
    • M. Benchohra, J.J. Nieto, and A. Ouahab Fuzzy solutions for impulsive differential equations Commun. Appl. Anal. 11 2007 379 394
    • (2007) Commun. Appl. Anal. , vol.11 , pp. 379-394
    • Benchohra, M.1    Nieto, J.J.2    Ouahab, A.3
  • 21
    • 41849120488 scopus 로고    scopus 로고
    • On new solutions of fuzzy differential equations
    • DOI 10.1016/j.chaos.2006.10.043, PII S0960077906010241
    • Y. Chalco-Cano, and H. Román-Flores On new solutions of fuzzy differential equations Chaos Solitons Fractals 38 2008 112 119 (Pubitemid 351503972)
    • (2008) Chaos, Solitons and Fractals , vol.38 , Issue.1 , pp. 112-119
    • Chalco-Cano, Y.1    Roman-Flores, H.2
  • 22
    • 0036642870 scopus 로고    scopus 로고
    • Brief note on the variation of constants formula for fuzzy differential equations
    • DOI 10.1016/S0165-0114(01)00158-0, PII S0165011401001580
    • P. Diamond Brief note on the variation of constants formula for fuzzy differential equations Fuzzy Sets and Systems 129 2002 65 71 (Pubitemid 34544383)
    • (2002) Fuzzy Sets and Systems , vol.129 , Issue.1 , pp. 65-71
    • Diamond, P.1
  • 23
    • 0002208128 scopus 로고    scopus 로고
    • Regularity of solution sets for differential inclusions quasi-concave in a parameter
    • P. Diamond, and P. Watson Regularity of solution sets for differential inclusions quasi-concave in a parameter Appl. Math. Lett. 13 2000 31 35
    • (2000) Appl. Math. Lett. , vol.13 , pp. 31-35
    • Diamond, P.1    Watson, P.2
  • 24
    • 79958115075 scopus 로고    scopus 로고
    • On Peano theorem for fuzzy differential equations
    • A.D.R. Choudary, and T. Donchev On Peano theorem for fuzzy differential equations Fuzzy Sets and Systems 177 2011 93 94
    • (2011) Fuzzy Sets and Systems , vol.177 , pp. 93-94
    • Choudary, A.D.R.1    Donchev, T.2
  • 28
    • 76549132342 scopus 로고    scopus 로고
    • A boundary value problem for second order fuzzy differential equations
    • A. Khastan, and J.J. Nieto A boundary value problem for second order fuzzy differential equations Nonlinear Anal. 72 2010 3583 3593
    • (2010) Nonlinear Anal. , vol.72 , pp. 3583-3593
    • Khastan, A.1    Nieto, J.J.2
  • 29
    • 79958159192 scopus 로고    scopus 로고
    • Variation of constant formula for first order fuzzy differential equations
    • A. Khastan, J.J. Nieto, and R. Rodríguez-López Variation of constant formula for first order fuzzy differential equations Fuzzy Sets and Systems 177 2011 20 33
    • (2011) Fuzzy Sets and Systems , vol.177 , pp. 20-33
    • Khastan, A.1    Nieto, J.J.2    Rodríguez-López, R.3
  • 30
    • 0000984385 scopus 로고
    • Remarks on Peano-like theorems for fuzzy differential equations
    • P.E. Kloeden Remarks on Peano-like theorems for fuzzy differential equations Fuzzy Sets and Systems 44 1991 161 163
    • (1991) Fuzzy Sets and Systems , vol.44 , pp. 161-163
    • Kloeden, P.E.1
  • 31
    • 0034668420 scopus 로고    scopus 로고
    • Uncertain systems and fuzzy differential equations
    • V. Lakshmikantham Uncertain systems and fuzzy differential equations J. Math. Anal. Appl. 251 2000 805 817
    • (2000) J. Math. Anal. Appl. , vol.251 , pp. 805-817
    • Lakshmikantham, V.1
  • 32
    • 0038137267 scopus 로고    scopus 로고
    • Interconnection between set and fuzzy differential equations
    • V. Lakshmikantham, S. Leela, and A.S. Vatsala Interconnection between set and fuzzy differential equations Nonlinear Anal. 54 2003 351 360
    • (2003) Nonlinear Anal. , vol.54 , pp. 351-360
    • Lakshmikantham, V.1    Leela, S.2    Vatsala, A.S.3
  • 33
    • 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 2003 255 268
    • (2003) Nonlinear Anal. , vol.55 , pp. 255-268
    • Lakshmikantham, V.1    Tolstonogov, A.A.2
  • 34
    • 0009756910 scopus 로고    scopus 로고
    • The cauchy problem for continuous fuzzy differential equations
    • PII S0165011497000948
    • J.J. Nieto The Cauchy problem for continuous fuzzy differential equations Fuzzy Sets and Systems 102 1999 259 262 (Pubitemid 129510837)
    • (1999) Fuzzy Sets and Systems , vol.102 , Issue.2 , pp. 259-262
    • Nieto, J.J.1
  • 35
    • 68749120554 scopus 로고    scopus 로고
    • Numerical solution of fuzzy differential equations under generalized differentiability
    • J.J. Nieto, A. Khastan, and K. Ivaz Numerical solution of fuzzy differential equations under generalized differentiability Nonlinear Anal. Hybrid Syst. 3 2009 700 707
    • (2009) Nonlinear Anal. Hybrid Syst. , vol.3 , pp. 700-707
    • Nieto, J.J.1    Khastan, A.2    Ivaz, K.3
  • 36
    • 24944547803 scopus 로고    scopus 로고
    • Bounded solutions for fuzzy differential and integral equations
    • DOI 10.1016/j.chaos.2005.05.012, PII S0960077905004790
    • J.J. Nieto, and R. Rodríguez-López Bounded solutions for fuzzy differential and integral equations Chaos Solitons Fractals 27 2006 1376 1386 (Pubitemid 41329831)
    • (2006) Chaos, Solitons and Fractals , vol.27 , Issue.5 , pp. 1376-1386
    • Nieto, J.J.1    Rodriguez-Lopez, R.2
  • 40
    • 45349112141 scopus 로고
    • On fuzzy differential equations
    • H. Ouyang, and Y. Wu On fuzzy differential equations Fuzzy Sets and Systems 32 1989 321 325
    • (1989) Fuzzy Sets and Systems , vol.32 , pp. 321-325
    • Ouyang, H.1    Wu, Y.2
  • 41
    • 40949090514 scopus 로고    scopus 로고
    • The RungeKutta method for hybrid fuzzy differential equations
    • S. Pederson, and M. Sambandham The RungeKutta method for hybrid fuzzy differential equations Nonlinear Anal. Hybrid Syst. 2 2008 626 634
    • (2008) Nonlinear Anal. Hybrid Syst. , vol.2 , pp. 626-634
    • Pederson, S.1    Sambandham, M.2
  • 42
    • 55949123641 scopus 로고    scopus 로고
    • Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem
    • S. Pederson, and M. Sambandham Numerical solution of hybrid fuzzy differential equation IVPs by a characterization theorem Inform. Sci. 179 2009 319 328
    • (2009) Inform. Sci. , vol.179 , pp. 319-328
    • Pederson, S.1    Sambandham, M.2
  • 43
    • 0036646539 scopus 로고    scopus 로고
    • Embedding of level-continuous fuzzy sets on Banach spaces
    • DOI 10.1016/S0020-0255(02)00182-2, PII S0020025502001822
    • H. Román-Flores, and M. Rojas-Medar Embedding of level-continuous fuzzy sets on Banach spaces Inform. Sci. 144 2002 227 247 (Pubitemid 34763557)
    • (2002) Information Sciences , vol.144 , Issue.1-4 , pp. 227-247
    • Roman-Flores, H.1    Rojas-Medar, M.2
  • 44
    • 0035285008 scopus 로고    scopus 로고
    • Differential equations with fuzzy parameters via differential inclusions
    • DOI 10.1006/jmaa.2000.7229, PII S0022247X00972299
    • T. Rzeuchowski, and J. Wasowski Differential equations with fuzzy parameters via differential inclusions J. Math. Anal. Appl. 255 2001 177 194 (Pubitemid 33383914)
    • (2001) Journal of Mathematical Analysis and Applications , vol.255 , Issue.1 , pp. 177-194
    • Rzezuchowski, T.1    Wasowski, J.2
  • 45
    • 0023581045 scopus 로고
    • On the fuzzy initial value problem
    • S. Seikkala On the fuzzy initial value problem Fuzzy Sets and Systems 24 1987 319 330
    • (1987) Fuzzy Sets and Systems , vol.24 , pp. 319-330
    • Seikkala, S.1
  • 46
    • 77951208686 scopus 로고    scopus 로고
    • A class of linear differential dynamical systems with fuzzy matrices
    • J. Xu, Z. Liao, and J.J. Nieto A class of linear differential dynamical systems with fuzzy matrices J. Math. Anal. Appl. 368 2010 54 68
    • (2010) J. Math. Anal. Appl. , vol.368 , pp. 54-68
    • Xu, J.1    Liao, Z.2    Nieto, J.J.3
  • 47
    • 6344232554 scopus 로고
    • Fuzzy random variables. Part I: Definitions and theorems
    • H. Kwakernaak Fuzzy random variables. Part I: definitions and theorems Inform. Sci. 15 1978 1 29
    • (1978) Inform. Sci. , vol.15 , pp. 1-29
    • Kwakernaak, H.1
  • 50
    • 0000565701 scopus 로고
    • The concept of normality for fuzzy random variables
    • M.L. Puri, and D.A. Ralescu The concept of normality for fuzzy random variables Ann. Probab. 13 1985 1373 1379
    • (1985) Ann. Probab. , vol.13 , pp. 1373-1379
    • Puri, M.L.1    Ralescu, D.A.2
  • 53
    • 33748063993 scopus 로고    scopus 로고
    • On Borel measurability and large deviations for fuzzy random variables
    • DOI 10.1016/j.fss.2005.03.014, PII S0165011406002041, Fuzzy Sets and Probability/Statistics Theory
    • P. Terán Agraz On Borel measurability and large deviations for fuzzy random variables Fuzzy Sets and Systems 157 2006 2558 2568 (Pubitemid 44301497)
    • (2006) Fuzzy Sets and Systems , vol.157 , Issue.19 , pp. 2558-2568
    • Teran Agraz, P.1
  • 54
    • 33750329419 scopus 로고    scopus 로고
    • Tools for fuzzy random variables: Embeddings and measurabilities
    • DOI 10.1016/j.csda.2006.04.017, PII S0167947306001162
    • M. López-Díaz, and D.A. Ralescu Tools for fuzzy random variables: embeddings and measurabilities Comput. Statist. Data Anal. 51 2006 109 114 (Pubitemid 44634802)
    • (2006) Computational Statistics and Data Analysis , vol.51 , Issue.1 , pp. 109-114
    • Lopez-Diaz, M.1    Ralescu, D.A.2
  • 55
    • 0242296087 scopus 로고    scopus 로고
    • Fuzzy stochastic differential systems
    • Y. Feng Fuzzy stochastic differential systems Fuzzy Sets and Systems 115 2000 351 363
    • (2000) Fuzzy Sets and Systems , vol.115 , pp. 351-363
    • Feng, Y.1
  • 56
    • 34447518790 scopus 로고    scopus 로고
    • Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients
    • DOI 10.1016/j.ins.2007.03.004, PII S0020025507001466
    • W. Fei Existence and uniqueness of solution for fuzzy random differential equations with non-Lipschitz coefficients Inform. Sci. 177 2007 4329 4337 (Pubitemid 47069313)
    • (2007) Information Sciences , vol.177 , Issue.20 , pp. 4329-4337
    • Fei, W.1
  • 57
    • 69249232212 scopus 로고    scopus 로고
    • On random fuzzy differential equations
    • M.T. Malinowski On random fuzzy differential equations Fuzzy Sets and Systems 160 2009 3152 3165
    • (2009) Fuzzy Sets and Systems , vol.160 , pp. 3152-3165
    • Malinowski, M.T.1
  • 58
    • 77953962287 scopus 로고    scopus 로고
    • Existence theorems for solutions to random fuzzy differential equations
    • M.T. Malinowski Existence theorems for solutions to random fuzzy differential equations Nonlinear Anal. 73 2010 1515 1532
    • (2010) Nonlinear Anal. , vol.73 , pp. 1515-1532
    • Malinowski, M.T.1
  • 59
    • 0001596637 scopus 로고    scopus 로고
    • Mean-square integral and differential of fuzzy stochastic processes
    • PII S016501149700119X
    • Y. Feng Mean-square integral and differential of fuzzy stochastic processes Fuzzy Sets and Systems 102 1999 271 280 (Pubitemid 129510839)
    • (1999) Fuzzy Sets and Systems , vol.102 , Issue.2 , pp. 271-280
    • Feng, Y.1
  • 60
    • 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
  • 61
    • 0001367476 scopus 로고
    • Lp metrics for compact, convex sets
    • Lp metrics for compact, convex sets J. Approx. Theory 45 1985 280 287
    • (1985) J. Approx. Theory , vol.45 , pp. 280-287
    • Vitale, R.A.1
  • 62
    • 49349119632 scopus 로고
    • A note on the extension principle for fuzzy sets
    • H.T. Nguyen A note on the extension principle for fuzzy sets J. Math. Anal. Appl. 64 1978 369 380
    • (1978) J. Math. Anal. Appl. , vol.64 , pp. 369-380
    • Nguyen, H.T.1
  • 63
    • 14344275700 scopus 로고    scopus 로고
    • The Peano theorem for fuzzy differential equations revisited
    • PII S0165011497004156
    • O. Kaleva The Peano theorem for fuzzy differential equations revisited Fuzzy Sets and Systems 98 1998 147 148 (Pubitemid 128654923)
    • (1998) Fuzzy Sets and Systems , vol.98 , Issue.1 , pp. 147-148
    • Kaleva, O.1
  • 68
    • 0000605531 scopus 로고
    • On embedding problems of fuzzy number space: Part 5
    • M. Ma On embedding problems of fuzzy number space: part 5 Fuzzy Sets and Systems 55 1993 313 318
    • (1993) Fuzzy Sets and Systems , vol.55 , pp. 313-318
    • Ma, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.