Advertisement

Solving Fuzzy Equations

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

Abstract

In this chapter we first look at different types of solutions to the simple fuzzy linear equation \(\bar A \cdot \bar X + \bar B = \bar C\) and then systems of fuzzy linear equations. Solving fuzzy differential equations, fuzzy difference equations and fuzzy integral equations, come later on in the book. In the applications section we also look at solving \(\bar A{\bar X^2} + \bar B\bar X = \bar C,\), the fuzzy quadratic. At the end of the chapter we discuss fuzzy input-output analysis. Solutions to more complicated fuzzy equations are discussed in ([2], [3], [6]). Throughout this chapter, except in Section 3.5, we use triangular, and triangular shaped, fuzzy numbers. In Section 3.5 we use trapezoidal (shaped) fuzzy numbers.

Keywords

Fuzzy Number Classical Solution Triangular Fuzzy Number Interval Arithmetic Final Demand 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    J.J. Buckley: Fuzzy Input-Output Analysis, European J. Operational Research, 39 (1989), pp. 54–60.CrossRefGoogle Scholar
  2. [2]
    J.J. Buckley: Solving Fuzzy Equations in Economics and Finance, Fuzzy Sets and Systems, 48 (1992), pp. 289–296.CrossRefGoogle Scholar
  3. [3]
    J.J. Buckley: Solving Fuzzy Equations, Fuzzy Sets and Systems, 50 (1992), pp. 1–14.CrossRefGoogle Scholar
  4. [4]
    J.J. Buckley and Y. Qu: Solving Linear and Quadratic Fuzzy Equations, Fuzzy Sets and Systems, 38 (1990), pp. 43–59.CrossRefGoogle Scholar
  5. [5]
    J.J. Buckley and Y. Qu: On Using Alpha—Cuts to Evaluate Fuzzy Equations, Fuzzy Sets and Systems, 38 (1990), pp. 309–312.CrossRefGoogle Scholar
  6. [6]
    J.J. Buckley and Y. Qu: Solving Fuzzy Equations: A New Solution Concept, Fuzzy Sets and Systems, 39 (1991), pp. 291–301.CrossRefGoogle Scholar
  7. [7]
    J.J. Buckley and Y. Qu: Solving Systems of Fuzzy Linear Equations, Fuzzy Sets and Systems, 43 (1991), pp. 33–43.CrossRefGoogle Scholar
  8. [8]
    J.J. Buckley, Th. Feuring and Y. Hayashi: Fuzzy Hierarchical Analysis Revisited, Proc. IFSA, Taipei, Taiwan, Aug. 17–20, 1999, Vol. 1, pp. 1–5.Google Scholar
  9. [9]
    J.J. Buckley, Th. Feuring and Y. Hayashi: Fuzzy Hierarchical Analysis, Proc. FUZZ-IEEE, Seoul, Korea, Aug. 22–25, 1999, Vol. 2, pp. 1009–1013.Google Scholar
  10. [10]
    J.J. Buckley, Th. Feuring and Y. Hayashi: Fuzzy Hierarchical Analysis Revisited, European J. Operational Research, 129 (2001), pp. 48–64.CrossRefGoogle Scholar
  11. [11]
    J.J. Buckley, Th. Feuring and Y. Hayashi: Fuzzy Eigenvalues, Fuzzy Sets and Systems. Under revision.Google Scholar
  12. [12]
    S.I. Grossman: Elementary Linear Algebra, Fifth Edition, Saunders, Forth Worth, Texas, 1994.Google Scholar
  13. [13]
    E. Hansen: On the Solution of Linear Equations with Interval Coefficients, Linear Algebra and its Applications, 2 (1969), pp. 153–165.CrossRefGoogle Scholar
  14. [14]
    R.E. Moore: Methods and Applications of Interval Analysis, SIAM Studies in Applied Mathematics, Philadelphia, 1979.CrossRefGoogle Scholar
  15. [15] M. Wagenknecht, R. Hampel and V. Schneider: Solving Linear Fuzzy Equation Systems (LFES)
    by Inclusion, Proc. IPUM, Madrid, Spain, July 3–7, 2000, pp. 1758–1763.Google Scholar
  16. [16]
    X. Wang and M. Ha: Solving a System of Fuzzy Linear Equations, in: M.Delgado, J.Kacprzyk, J.-L. Verdegay and M.A.Vila (eds.), Fuzzy Optimization, Physica-Verlag, Heidelberg, 1994, pp. 102–108.Google Scholar
  17. [17]
    W. Wang, Z. Zhong and M. Ha: Iteration Algorithm for Solving a System of Fuzzy Linear Equations, Fuzzy Sets and Systems, 119 (2001), pp. 121–128.CrossRefGoogle 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

Personalised recommendations