Applications of fuzzy Laplace transforms

A natural way to model dynamic systems under uncertainty is to use fuzzy initial value problems (FIVPs) and related uncertain systems. In this paper, we express the fuzzy Laplace transform and then some of its well-known properties are investigated. In addition, an existence theorem is given for fuzzy-valued function which possess the fuzzy Laplace transform. Consequently, we investigate the solutions of FIVPs and the solutions in state-space description of fuzzy linear continuous-time systems under generalized H-differentiability as two new applications of fuzzy Laplace transforms. Finally, some examples are given to show the efficiency of the proposed method.

[1]  Tofigh Allahviranloo,et al.  Nth-order fuzzy linear differential equations , 2008, Inf. Sci..

[2]  Tofigh Allahviranloo,et al.  Euler method for solving hybrid fuzzy differential equation , 2011, Soft Comput..

[3]  S. Seikkala.  On the fuzzy initial value problem , 1987 .

[4]  P. Kloeden.  Remarks on Peano-like theorems for fuzzy differential equations , 1991 .

[5]  M. Puri,et al.  DIFFERENTIAL FOR FUZZY FUNCTION , 1983 .

[6]  Derong Liu,et al.  Stability and Control of Dynamical Systems With Applications: A Tribute to Anthony N. Michel (Control Engineering (Birkhauser).) , 2004 .

[7]  Osmo Kaleva.  Fuzzy differential equations , 1987 .

[8]  Juan J. Nieto,et al.  Linear First-Order Fuzzy Differential Equations , 2006, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[9]  Tofigh Allahviranloo,et al.  Fuzzy Laplace transforms , 2009, Soft Comput..

[10]  Jiuping Xu,et al.  A class of linear differential dynamical systems with fuzzy matrices , 2010 .

[11]  M. Puri,et al.  Differentials of fuzzy functions , 1983 .

[12]  Tofigh Allahviranloo,et al.  Toward the existence and uniqueness of solutions of second-order fuzzy differential equations , 2009, Inf. Sci..

[13]  B. Bede,et al.  Fuzzy Differential Equations in Modeling of Hydraulic Differential Servo Cylinders , 2006 .

[14]  Zuohua Ding,et al.  Existence of the Solutions of Fuzzy Differential Equations with Parameters , 1997, Inf. Sci..

[15]  Saeid Abbasbandy,et al.  Numerical methods forfuzzy differential inclusions , 2004 .

[16]  Imre J. Rudas,et al.  First order linear fuzzy differential equations under generalized differentiability , 2007, Inf. Sci..

[17]  Xiaoping Xue,et al.  The oscillation of delay differential inclusions and fuzzy biodynamics models , 2003 .

[18]  A. Khastan,et al.  New Results on Multiple Solutions for th-Order Fuzzy Differential Equations under Generalized Differentiability , 2009 .

[19]  Hans-Jürgen Zimmermann,et al.  Fuzzy Set Theory - and Its Applications , 1985 .

[20]  Phil Diamond,et al.  Time-dependent differential inclusions, cocycle attractors and fuzzy differential equations , 1999, IEEE Trans. Fuzzy Syst..

[21]  H. Román-Flores,et al.  On new solutions of fuzzy differential equations , 2008 .

[22]  Saeid Abbasbandy,et al.  NUMERICAL METHODS FOR FUZZY DIFFERENTIAL INCLUSIONS , 2004 .

[23]  Xiaoping Xue,et al.  Impulsive functional differential inclusions and fuzzy population models , 2003, Fuzzy Sets Syst..

[24]  Abraham Kandel,et al.  Numerical solutions of fuzzy differential and integral equations , 1999, Fuzzy Sets Syst..

[25]  Tofigh Allahviranloo,et al.  A new method for solving fuzzy linear differential equations , 2011, Computing.

[26]  Jiuping Xu,et al.  A class of linear differential dynamical systems with fuzzy initial condition , 2007, Fuzzy Sets Syst..

[27]  R. Goetschel,et al.  Topological properties of fuzzy numbers , 1983 .

[28]  D. Dubois,et al.  Towards fuzzy differential calculus part 3: Differentiation , 1982 .

[29]  Sorin G. Gal,et al.  Almost periodic fuzzy-number-valued functions , 2004, Fuzzy Sets Syst..

[30]  Lotfi A. Zadeh,et al.  On Fuzzy Mapping and Control , 1996, IEEE Trans. Syst. Man Cybern..

[31]  Azriel Rosenfeld,et al.  Geodesic Visibility in Graphs , 1998, Inf. Sci..

[32]  V. Lakshmikantham,et al.  Revisiting fuzzy differential equations , 2004 .

[33]  Osmo Kaleva.  The Cauchy problem for fuzzy differential equations , 1990 .

[34]  Congxin Wu,et al.  Existence Theorem to the Cauchy Problem of Fuzzy Differential Equations under Compactness-Type Conditions , 1998, Inf. Sci..

[35]  Tofigh Allahviranloo,et al.  Numerical solution of fuzzy differential equations by predictor-corrector method , 2007, Inf. Sci..

[36]  M. Puri,et al.  Fuzzy Random Variables , 1986 .

[37]  Shiji Song,et al.  Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations , 2000, Fuzzy Sets Syst..

[38]  Panos J. Antsaklis,et al.  A Linear Systems Primer , 2007 .

[39]  Barnabás Bede,et al.  Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations , 2005, Fuzzy Sets Syst..

[40]  Hsien-Chung Wu,et al.  The Improper Fuzzy Riemann Integral and its Numerical Integration , 1998, Inf. Sci..

[41]  Dimitris N. Georgiou,et al.  Initial value problems for higher-order fuzzy differential equations , 2005 .