Towards the theory of fuzzy differential equations

Comparative analysis of two ideologically distinct approaches in the theory of fuzzy differential equations is given. Domains of applications, advantages and shortcomings of those approaches are described. New definitions of solutions to fuzzy differential equations are proposed.

[1]  Eyke Hüllermeier,et al.  An Approach to Modelling and Simulation of Uncertain Dynamical Systems , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[2]  Phil Diamond,et al.  Stability and periodicity in fuzzy differential equations , 2000, IEEE Trans. Fuzzy Syst..

[3]  P. Kloeden,et al.  Metric Spaces Of Fuzzy Sets Theory And Applications , 1975 .

[4]  E. Kamke Zur Theorie der Systeme gewöhnlicher Differentialgleichungen. II. , 1932 .

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

[6]  V. A. Baidosov FUZZY DIFFERENTIAL INCLUSIONS , 1990 .

[7]  Stanley P. Gudder Connectives and fuzziness for classical effects , 1999, Fuzzy Sets Syst..

[8]  Osmo Kaleva Fuzzy differential equations , 1987 .

[9]  James J. Buckley,et al.  Fuzzy differential equations , 2000, Fuzzy Sets Syst..

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

[11]  R. Leland Fuzzy differential systems and Malliavin calculus , 1995 .

[12]  Hung T. Nguyen,et al.  A note on the extension principle for fuzzy sets , 1978 .

[13]  J P Aubin FUZZY DIFFERENTIAL INCLUSIONS , 1990 .

[14]  Bennet P. Lientz,et al.  On time dependent fuzzy sets , 1972, Inf. Sci..

[15]  Osmo Kaleva The Peano theorem for fuzzy differential equations revisited , 1998, Fuzzy Sets Syst..

[16]  Abraham Kandel,et al.  On the validity of the Peano theorem for fuzzy differential equations , 1997, Fuzzy Sets Syst..

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

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

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

[20]  Abraham Kandel,et al.  Comments on "The peano theorem for fuzzy differential equations revisited" , 1998, Fuzzy Sets Syst..