AN ABS-FRE ALGORITHM FOR SOLVING SYSTEMS OF FUZZY RELATION EQUATIONS

  • Xia, Zun-Quan (Laboratory 2, CORA, Department of Applied Mathematics, Dalian University of Technology) ;
  • Guo, Fang-Fang (Laboratory 2, CORA, Department of Applied Mathematics, Dalian University of Technology)
  • Published : 2004.05.01

Abstract

The general scheme of an algorithm, called an ABS-FRE algorithm, for solving systems of fuzzy relation equations (systems of FRE) via the ABS algorithms is presented. As special cases, two particular algorithms for obtaining the greatest and minimal solutions of systems of FRE are described. Several new operations used in this scheme are given, for instance, operators $\veebar$ and $\underline{\wedge}$ called quasi-inverses of operators $\vee$ and $\wedge$, respectively, etc.

Keywords

References

  1. ABS Projection Algorithms: Mathematical Techniques for Linear and Nonlinear Algebraic Equations J. Abaffy;E. Spedicato
  2. Fuzzy Sets and Systems v.88 A new lood at solving a system of fuzzy relational equations F. L. Chung;T. Lee
  3. Fuzzy Sets and Systems v.103 Novel neural algorithms based on fuzzy 6 rules for solving fuzzy relation equations X. Li;D. Ruan
  4. Introduction to fuzzy sets Luo C.
  5. Fuzzy Sets and Systems v.49 Fuzzy linear systems K.Peeva
  6. Fuzzy Sets and Systems v.40 Processing in relational structure: Fuzzy relational equations W. Pedrycz
  7. Information and Control v.30 Resolusion of composite fuzzy relation equations E. Sanche
  8. Surveys on Mathematics for Industry v.3 Ten years of ABS methods: a review of theoretical results and computational achievements E. Spedicato
  9. QDMSIA2001/01, University of Bergamo Twenty years of ABS algorithms: a bibliography E. Spedicato
  10. Applications in Science and Engineering, Series C: Mathemitical and Physical Science v.508 ABS algorithms for linear equations and applications to optimazation E. Spedicato;Z.-O. Xia;L.-W. Zhang
  11. J. of Computational and Applied Mathematics v.124 ABS algorithms for linear equations and optimization E. Spedicato;Z. Xia;L. Zhang