# FUZZY r-MINIMAL α-OPEN SETS ON FUZZY MINIMAL SPACES

Min, Won-Keun

• Published : 2012.07.31
• 25 2

#### Abstract

We introduce the concept of fuzzy $r$-minimal ${\alpha}$-open set on a fuzzy minimal space and some basic properties. We also introduce the concepts of fuzzy $r$-M ${\alpha}$-continuous and fuzzy $r$-M($M^*$) ${\alpha}$-open mappings, and investigate characterization for such mappings.

#### Keywords

r-minimal semiopen;r-minimal ${\alpha}$-open;fuzzy r-M continuous;fuzzy r-M ${\alpha}$-continuous;fuzzy r-M semicontinuous;r-M($M^*$) ${\alpha}$-open mappings

#### References

1. C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190. https://doi.org/10.1016/0022-247X(68)90057-7
2. W. K. Min and M. H. Kim, Fuzzy r-minimal semiopen sets and fuzzy r-M semicontinuous functions on fuzzy r-minimal spaces, Proceedings of KIIS Spring Conference 2009, 19 (1) (2009), 49-52.
3. A. A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems 48 (1992), no. 3, 371-375. https://doi.org/10.1016/0165-0114(92)90352-5
4. Y. H. Yoo, W. K. Min, and J. I. Kim, Fuzzy r-minimal structures and fuzzy r-minimal spaces, Far East J. Math. Sci. 33 (2009), no. 2, 193-205.
5. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X