Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Equivalence Relations

  • Kim, Yong-Chan (Department of Mathematics, Kangnung National University) ;
  • Kim, Young-Sun (Department of Applied Mathematics, Pai Chai University)
  • Published : 2008.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

We investigate the properties of fuzzy relations and $\odot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, fuzzy relations preserve(*, \otimes$)-equivalence relations where $\otimes$ are compositions, $\Rightarrow$ and $\Leftarrow$.

Keywords

References

  1. R. Belohlavek, Similarity relations inconcept lattices, J. Logic and Computation 10 (6) (2000) 823-845 https://doi.org/10.1093/logcom/10.6.823
  2. R. Belohlavek, Fuzzy equationallogic, Arch. Math. Log. 41 (2002) 83-90 https://doi.org/10.1007/s001530200006
  3. R. Belohlavek, Similarity relations and BK-relational products, Information Sciences 126 (2000) 287-295 https://doi.org/10.1016/S0020-0255(99)00149-8
  4. J. Y. Girard, Linear logic, Theoret. Comp. Sci. 50, 1987, 1-102 https://doi.org/10.1016/0304-3975(87)90045-4
  5. P.Hajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht (1998)
  6. U. Hohle, Many valued topology and its applications, Kluwer Academic Publisher, Boston, (2001)
  7. U. Hohle, E. P. Klement, Non-classical logic and their applications to fuzzy subsets, Kluwer Academic Publisher, Boston,1995
  8. U. Hohle, S. E. Rodabaugh, Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, Volume 3, Kluwer Academic Publishers, Dordrecht (1999)
  9. J. Jacas,J.Recasens, Fuzzy T-transitive relations: eigenvectors and generators, Fuzzy Sets and Systems 72 (1995) 147-154 https://doi.org/10.1016/0165-0114(94)00347-A
  10. Liu Ying-Ming, Projective and injective objects in the category of quantales, J. of Pure and Applied Algebra, 176, 2002, 249-258 https://doi.org/10.1016/S0022-4049(02)00064-6
  11. C.J. Mulvey, Quantales, Suppl. Rend. Cric. Mat. Palermo Ser.II 12,1986, 99-104
  12. C.J. Mulvey, J. W. Pelletier, On the quantisation of point, J. of Pure and Applied Algebra,159, 2001, 231-295 https://doi.org/10.1016/S0022-4049(00)00059-1
  13. S. E.Rodabaugh, E. P. Klement, Toplogical And Algebraic Structures In Fuzzy Sets, The Handbook of Recent Developments in the Mathematics of Fuzzy Sets, Trendsin Logic 20, Kluwer Academic Publishers,(Boston/Dordrecht/London)(2003)
  14. E. Turunen, Mathematics Behind Fuzzy Logic, A Springer-Verlag Co.,1999