Fuzzy Difference Equations

  • James J. Buckley
  • Esfandiar Eslami
  • Thomas Feuring
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 91)


In this chapter we are concerned with solutions to the second order, linear, constant coefficient difference equation
for k = 0,1, 2,..., where a, b are constants with b > 0 and g(x) is continuous for x > O. The initial conditions are y(0) = γ0 and y(1) = γl. We will fuzzify the difference equation by considering fuzzy initial conditions , for triangular fuzzy numbers and .


Difference Equation Fuzzy Number Classical Solution Partial Solution National Income 
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  1. [1]
    J.J. Buckley, Th. Feuring and Y. Hayashi: Fuzzy Difference Equations: The Initial Value Problem. J. Advanced Computational Intelligence. To appear.Google Scholar
  2. [2]
    E.Y. Deeba and A. de Korvin: On a Fuzzy Difference Equation, IEEE Trans. Fuzzy Systems, 3 (1995), pp. 469–473.CrossRefGoogle Scholar
  3. [3]
    E.Y. Deeba and A. de Korvin: Analysis by Fuzzy Difference Equations of a Model of CO2 Level in the Blood, Applied Math. Letters, 12 (1999), pp. 33–40.CrossRefGoogle Scholar
  4. [4]
    E. Deeba, A. de Korvin and S. Xie: Techniques and Applications of Fuzzy Set Theory to Difference and Functional Equations and their Utilization in Modeling Diverse Systems, in: C.T. Leondes (Ed.), Fuzzy Theory Systems, Vol. 1, Academic Press, San Diego, CA., pp. 87–110.Google Scholar
  5. [5]
    The Fibonacci Quarterly, Fibonacci Association, Univ. Santa Clara, CA.Google Scholar
  6. [6]
    S. Goldberg: Introduction to Difference Equations, John Wiley and Sons, N. Y., 1958.Google Scholar
  7. [7]
    F.B. Hildebrand: Methods of Applied Mathematics, Prentice Hall, Englewood Cliffs, N.J., 1958.Google Scholar
  8. [8]
    F.B. Hildebrand: Finite—Difference Equations and Simulations, Prentice Hall, Englewood Cliffs, N.J., 1968.Google Scholar
  9. [9]
    W.G. Kelley and A.C. Peterson: Difference Equations: An Introduction with Applications, Second Edition, Harcourt/Academic Press, Burlington, MA, USA, 2000.Google Scholar
  10. [10]
    V. Lakashmikanthan and D. Trigante: Theory of Difference Equations, Academic Press, San Diego, CA, 1988.Google Scholar
  11. [11]
    K.S. Miller: Linear Difference Equations, W.A. Benjamin, N.Y., 1968.Google Scholar
  12. [12]
    P.A. Samuelson: Interactions Between the Multiplier Analysis and the Principle of Acceleration, Review of Economic Statistics, 21 (1939), pp. 75–78.CrossRefGoogle Scholar
  13. [13]
    C.E. Shannon and W. Weaver: The Mathematical Theory of Communication, Univ. of Illinois Press, Urbana, Ill., 1949.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • James J. Buckley
    • 1
  • Esfandiar Eslami
    • 2
  • Thomas Feuring
    • 3
  1. 1.Mathematics DepartmentUniversity of Alabama at BirminghamBirminghamUSA
  2. 2.Department of MathematicsShahid Bahonar UniversityKermanIran
  3. 3.Electrical Engineering and Computer ScienceUniversity of SiegenSiegenGermany

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