International Journal of Fuzzy Logic and Intelligent Systems

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

DOI QR Code

Fuzzy Relations and Metrics

  • Kim, Yong-Chan (Department of Mathematics, Kangnung National University) ;
  • Kim, Young-Sun (Department of Applied Mathematics, Pai Chai University)
  • Published : 2009.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

We investigate the properties of fuzzy relations, metrics and $\bigodot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, pseudo-(quasi-) metrics induce $\bigodot$-(quasi)-equivalence relations.

Keywords

References

  1. M. De Baets, R. Mesiar, "Psedo-metrics and Tequivalences," J. Fuzzy. Math., vol. 5, pp. 471-481, 1997
  2. M. De Baets, R. Mesiar, "Metrics and $\tau$-equalities," J. Math. Anal., vol. 267, pp. 531-547, 2002 https://doi.org/10.1006/jmaa.2001.7786
  3. R. B$\check{e}$lohl$\acute{a}$vek, "Similarity relations and BK-relational products," Information Sciences, vol. 126, pp. 287-295, 2000 https://doi.org/10.1016/S0020-0255(99)00149-8
  4. J.Y. Girard, " Linear logic," Theoret. Comp. Sci., vol. 50, pp. 1-102, 1987 https://doi.org/10.1016/0304-3975(87)90045-4
  5. P. H$\acute{a}$kek, Metamathemaices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998
  6. U. H$\ddot{o}$hle, Many valued topology and its applications, Kluwer Academic Publisher, Boston, 2001
  7. U. H$\ddot{o}$hle, E. P. Klement, Non-classical logic and their applications to fuzzy subsets , Kluwer Academic Publisher, Boston, 1995
  8. U. H$\ddot{o}$hle, 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, vol.72, pp. 147-154, 1995 https://doi.org/10.1016/0165-0114(94)00347-A
  10. J.M. Ko, Y.C. Kim, " The properties of fuzzy relations," submit to J. Korea Institute pf lntelligent Systems
  11. C.J. Mulvey, "Quantales," Suppl. Rend. Cric. Mat. Palermo Ser.lI, vol. 12, pp. 99-104, 1986
  12. C.J. Mulvey， J.W. Pelletier, "On the quantisation of point," J. of Pure and Applied Algebra, vol. 159, pp. 231-295, 2001 https://doi.org/10.1016/S0022-4049(00)00059-1
  13. H.T. Nguyen and E.A. Walker, Fuzzy logic, Chapman and Hall, New York, 2000