Properties of Double Fuzzy $b$-Open Sets

Abstract

In this paper, we introduce and study the concept of $(r, s)$-fuzzy $b$-border, $(r, s)$-fuzzy $b$-exterior and $(r, s)$-fuzzy $b$-frontier. Some of its interesting properties and characterizations are examined.

Keywords

• Double fuzzy topology
• (r; s)-fuzzy b-open set
• (r; s)- fuzzy b-closed set.

References

1. [1] K. Atanassov, New operators defined over the intuitionistic fuzzy sets, Fuzzy Sets and Sysetms, 61, No. 2 (1993), 137-142.
2. [2] C. L. Chang, Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24, No. 1 (1968), 182-190.
3. [3] D. Coker, An introduction to fuzzy subspaces in intuitionistic topological spaces, J. Fuzzy Math., 4 (1996), 749-764.
4. [4] D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88, No. 1 (1997), 81-89.
5. [5] M. Demirci, D. Coker, An introduction to intuitionistic fuzzytopological spaces in Sostak’s sense, Busefal 67 (1996), 67-76.
6. [6] Fatimah. M. Mohammed, M. S. M. Noorani and A. Ghareeb, Generalized b-closed sets and b-open sets in double fuzzy topological spaces, AIP Conference Proceedings, 1602, (2015), 909-917.
7. [7] J. Gutierrez Garcia and S. E. Rodabaugh, Order-theoretic, topological, categorical re-dundancies of interval-valued sets, grey sets, vague sets, interval-valued; intuitionistic sets, intuitionistic fuzzy sets and topologies, Fuzzy Sets and Systems, 156, No. 3 (2005),445-484.
8. [8] E. P. Lee and Y. B. Im., Mated fuzzy topological spaces, Journal of fuzzy logic and intelligent systems, 11 (2001), 161-165.

9. [9] S. K. Samanta and T. K. Mondal, On intuitionistic gradation of openness, Fuzzy Sets and Systems, 131, No. 3 (2002), 323-336.
10. [10] L. A. Zadeh, Fuzzy sets, Information and Control, 8, No. 3 (1965), 338-353.