Document Type : Research Paper
Authors
- Appachi Vadivel ^{} ^{}
- Elangovan Elavarasan ^{}
Department of Mathematics, Annamalai University, Annamalai Nagar-608002, Tamil Nadu, India.
Abstract
In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the relationship among fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Finally, we have given some counter examples to show that these types of mappings are not equivalent.
Keywords
- $r$-fuzzy regular semi open (closed) sets
- $r$-fuzzy regular semi interior (closure) operator
- Fuzzy regular semi continuous (irresolute) maps
Main Subjects
[2] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968) 182-190.
[3] K.C. Chattopadhyay and S.K. Samanta, Fuzzy topology, Fuzzy Sets and Systems, 54 (1993) 207-212.
[4] K.C. Chattopadhyay, R.N. Hazra, and S.K. Samanta, Gradation of openness, Fuzzy Sets and Systems, 49 (2) (1992) 237-242.
[5] R.N. Hazra, S.K. Samanta, and K.C. Chattopadhyay, Fuzzy topology redefined, Fuzzy Sets and Systems, 45 (1992) 79-82.
[6] E.E. Kerre and M.A. Fath Alla, On fuzzy regular semi open sets and $alpha S^{*}$-closed fuzzy topological spaces, The Journal of Fuzzy Mathematics, 11 (1) (2003) 225-235.
[7] S.J. Lee and E.P. Lee, Fuzzy $r$-regular open sets and fuzzy almost $r$-continuous maps, Bull. Korean Math. Soc., 39 (3) (2002) 441-453.
[8] A.S. Mashhour, M.H. Ghanim, and M.A. Fath Alla, $alpha$-separation axioms and $alpha$-compactness in fuzzy topological spaces, Rocky Moutain Journal of Mathematics, 16 (3) (1986) 591-600.
[9] A.A. Ramadan, Smooth topological spaces, Fuzzy Sets and Systems, 48 (1992) 371-375.
[10] A.A. Ramadan, S.E. Abbas, and Y.C. Kim, Fuzzy irresolute mappings in smooth fuzzy topological spaces, The Journal of Fuzzy Mathematics, 9 (4) (2001) 865-877.
[11] A.P. Šostak, On a fuzzy topological structure, Rend. Circ. Matem. Palermo Ser II, 11 (1986), 89-103.
[12] A. Vadivel and E. Elavarasan, Applications of $r$-generalized regular fuzzy closed sets, Annals of Fuzzy Mathematics and Informatics, (Accepted).
[13] A.M. Zahran, Fuzzy regular semi open sets and $alpha S$-closed spaces, The Journal of Fuzzy Mathematics, 2 (4) (1997), 579-586.