Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Interval-Valued Fuzzy Relations

  • Hur, Kur (Division of Mathematics and Informational Statistics, Nanoscale Sciences and Technology Institute, Wonkwang University) ;
  • Lee, Jeong-Gon (Division of Mathematics and Informational Statistics, Nanoscale Sciences and Technology Institute, Wonkwang University) ;
  • Choi, Jeong-Yeol (Division of Mathematics and Informational Statistics, Nanoscale Sciences and Technology Institute, Wonkwang University)
  • Received : 2009.01.22
  • Accepted : 2009.05.19
  • Published : 2009.06.25
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Abstract

By using the notion of interval-valued fuzzy relations, we forms the poset (IVFR (X), $\leq$) of interval-valued fuzzy relations on a given set X. In particular, we forms the subposet (IVFE (X), $\leq$) of interval-valued fuzzy equivalence relations on a given set X and prove that the poset (IVFE(X), $\leq$) is a complete lattice with the least element and greatest element.

Keywords

Acknowledgement

Supported by : Wonkwang University

References

  1. K. Atanassov, 'Intuitionistic fuzzy Sets', Fuzzy Sets and Systems, 20, 87-96, 1986 https://doi.org/10.1016/S0165-0114(86)80034-3
  2. R.Biawas, 'Rosenfeld's fuzzy subgroups with interval-valued membership functions', Fuzzy Sets and Systems, 63, 87-90, 1994 https://doi.org/10.1016/0165-0114(94)90148-1
  3. M.B Gorzalzany, 'A method of inference in approx-imate reasoning based on interval-valued fuzzysets', Fuzzy Sets and Systems, 21, 1-17, 1987 https://doi.org/10.1016/0165-0114(87)90148-5
  4. Y. B. Jun, J. J. Bae, S. H. Cho and C. S. Kim, 'Interval-valued fuzzy strong semi-openness and interval-valued fuzzy strong semi-continuity', Honam Math. J., 28, no.3, 417-431, 2006
  5. T. K. Mondal and S. K. Samanta, 'Topology of interval fuzzy sets', Indian J. PureAppl. Math., 30, no. 1, 23-38, 1999
  6. T. K. Mondal and S. K. Samanta, 'Connectedness in topology of interval-valued fuzzy sets', Italian J. Pure Appl. Math., 18, 33-50, 2005
  7. J. H. Park, J. S. Park and Y. C. Kwun, 'On fuzzy inclusion in the interval-valued sense', FSKG 2005, LANI 3613, Springer-Verlag, 1-10, 2005
  8. P. V. Ramakrishnan and V. Lakshmana Gomathi Nayagam,'Hausdorff interval-valued fuzzy¯lters', J. Korean Math.Soc., 39, no.1, 137-148, 2002 https://doi.org/10.4134/JKMS.2002.39.1.137
  9. M. K. Roy and R. Biswas, 'I-v fuzzy relations and Sanchez's approach for medical diagnosis', Fuzzy Sets and Systems, 47, 35-38, 1992 https://doi.org/10.1016/0165-0114(92)90057-B
  10. W. Zeng and Y. Shi, 'Note on interval-valued fuzzy set', FSKG 2005, LANI 3613, Springer-Verlag, 20-25, 2005
  11. L. A. Zadeh, 'Fuzzy sets', Inform. Control, 8, 338-353, 1965 https://doi.org/10.1016/S0019-9958(65)90241-X
  12. L. A. Zadeh, 'The concept of a linguistic variable and its application to approximate reasoning I', In-form, Sci., 8, 199-249, 1975

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