Review on Fuzzy Difference Equation


  • Mukminah Darus
  • Abd Fatah Wahab



Fuzzy difference equation, Type-2 fuzzy, Finance,


Fuzzy difference equation has been introduced by Kandel and Byatt in 1978. This topic has been growing rapidly for many years. Fuzzy difference forms is suitable for uncertainty or vagueness problems such as mathematical modelling, finance or else and it also applied in engineering, economics, science and etc. In this paper, we review the application of fuzzy difference equations that has been used before. We also give some ideas to relate from this type-1 fuzzy difference equation to type-2 fuzzy. The using of type-2 fuzzy is for more uncertainties and it is really suitable for problems in finance.


L. A. Zadeh, Fuzzy Sets, inform. Control 8 (1965), 338-353.

S. S. L. Chang, L. Zadeh, IEEE Trans System Man Cybernet, 2 (1972), 30-34.

A. Kandel, W. J. Byatt, Proc. Int. Conf. Cybernatics and Society, Tokyo, Novenber 1978, 1213-1216.

A. Kandel, W. J. Byatt, Proc. IEEE, 66 (1978), 1619-1639.

O. Kaleva, Fuzzy Sets and Systems, 24 (1987), 301-317.

O. Kaleva, Fuzzy Sets and System, 35 (1990), 389-396.

Q. Zhang, L. Yang, D. Liao, Engineering and Technology, 75 (2011).

K. A. Chrysafis, B. K. Papadopoulos, and G. Papaschinopoulos, Fuzzy Sets and Systems, 159 (2008), 3259-3270.

J. J. Buckly, Fuzzy Sets and Systems, 21 (3) (1987), 257-273. [10] L. A. Zadeh, Inform. Sci., 8 (1975), 199-249. [11] E. Y. Deeba and A. De Korvin, Applied Mathematics Latters, 12 (1999), 33-40. [12] G. Papaschinopoulos and B. K. Papadopoulos, Soft. Compt., 6(2002), 456-461.

G. Papaschinopoulos, G. Stefanidou and P. Efraimidis, Information Sciences, 177(2007), 3855-3870.

Jerry M. Mendel and Robert I. Bob John, IEEE Transaction on Fuzzy Systems, 10 (2002), 117-125.

G. Stefanidou and G. Papaschinopoulos, Fuzzy Sets and System, 2004, 337-357.

Snezhana Gocheva-Ilieva, Plovdia University.

Zehua Lv, Hai Jin, and Pingpeng Yuan, IEEE Computer and Information Technology, 2009.