# INTERVAL-VALUED FUZZY CONTRA ALPHA-CONTINUOUS MAPPINGS

Jun, Young-Bae;Jeong, Seong-Woo;Lee, Hyeon-Jeong;Lee, Joon-Woo

• Accepted : 2008.04.23
• Published : 2008.06.25
• 26 7

#### Abstract

The notion of interval-valued fuzzy ${\alpha}$-continuous mappings and interval-valued fuzzy contra ${\alpha}$-continuous mappings is introduced, and their characterizations are investigated.

#### Keywords

Interval-valued fuzzy topological space;interval-valued fuzzy contra continuous mapping;interval-valued fuzzy contra ${\alpha}$-continuous mapping

#### References

1. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
2. K. K. Azad, On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal App. 82 (1981), 14-32. https://doi.org/10.1016/0022-247X(81)90222-5
3. R. Biawas, Rosenfeld's fuzzy subgroups with interval-valued membership functions, Fuzzy Sets and Systems 63 (1994), 87-90. https://doi.org/10.1016/0165-0114(94)90148-1
4. E. Ekici and E. E. Lerre, On fuzzy contra-continuities, Advances Fuzzy Math. 1 (2006), no. 1, 35-44.
5. M. B. Gorzalczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems 21 (1987), 1-17. https://doi.org/10.1016/0165-0114(87)90148-5
6. Y. B. Jun, J. H. 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 (2006), no. 3, 417-431.
7. Y. B. Jun, S. W. Jeong, H. J. Lee and J. W. Lee, Interval-valued fuzzy contra alpha-open mappings, Honam Math. J. (submitted). https://doi.org/10.5831/HMJ.2008.30.2.283
8. Y. B. Jun, G. C. Kang and M. A. Ozturk, Interval-valued fuzzy semiopen, preopen and $\alpha$-open mappings, Honam Math. J. 28 (2006), no. 2, 241-259.
9. T. K. Mondal and S. K. Samanta, Topology of interval-valued fuzzy sets, Indian J. Pure Appl. Math. 30 (1999), no. 1, 23-38.
10. T. K. Mondal and S. K. Samanta, Connectedness in topology of interval-valued fuzzy sets, Italian J. Pure Appl. Math. 18 (2005), 33-50.
11. J. H. Park, J. S. Park and Y. C. Kwun, On fuzzy inclusion in the interval-valued sense, FSKD 2005, LNCS 3613, Springer-Verlag (2005), 1-10.
12. P. V. Ramakrishnan and V. Lakshmana Gomathi Nayagam, Hausdorff interval valued fuzzy filters, J. Korean Math. Soc. 39 (2002), no. 1, 137-148. https://doi.org/10.4134/JKMS.2002.39.1.137
13. M. K. Roy and R. Biswas, I-v fuzzy relations and Sanchez's approach for medical diagnosis, Fuzzy Sets and Systems 47 (1992), 35-38. https://doi.org/10.1016/0165-0114(92)90057-B
14. W. Zeng and Y. Shi, Note on interval-valued fuzzy set, FSKD 2005, LNCS 3613, Springer-Verlag (2005), 20-25.
15. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
16. L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning I, Inform. Sci. 8 (1975), 199-249. https://doi.org/10.1016/0020-0255(75)90036-5