Document Type: Research Paper
Authors
- Appachi Vadivel ^{} ^{1}
- Elangovan Elavarasan ^{} ^{2}
^{1} Department of Mathematics, Annamalai University, Annamalainagar, Tamil Nadu-608 002, India.
^{2} Research scholar, Department of Mathematics, Annamalai University, Annamalainagar, Tamil Nadu-608 002, India.
Abstract
In this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of A.P. Sostak's and Ramadan is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.
Keywords
- Rarely generalized regular fuzzy continuous
- Grf-compact space
- Rarely grf-almost compact space
- Rarely grf-$T_{2}$-spaces
Main Subjects
[1] B. Amudhambigai, M.K. Uma, and E. Roja, On rarely $widetilde{g}$-continuous functions in smooth fuzzy topological spaces, The Journal of Fuzzy Mathematics., 20 (2) (2012) 433-442.
[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] S. Jafari, A note on rarely continuous functions, Univ. Bacau. Stud. Cerc. St. Ser. Mat., 5 29-34.
[5] S. Jafari, On some properties of rarely continuous functions, Univ. Bacau. Stud. Cerc. St. Ser. Mat., 7 65-73.
[6] 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.
[7] N. Levine, Decomposition of continuity in topological spaces, Amer. Math. Monthly., 60 44-46.
[8] P.E. Long and L.L. Herrington, Properties of rarely continuous functions, Glasnik Math., 17 (37) 147-153.
[9] R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl., 56 (1976) 621-633.
[10] V. Popa, Sur certain decompositionde la continuite dans les espaces topologiques, Glasnik Mat. Setr III., 14 (34) 359-362.
[11] A.A. Ramadan, S.E. Abbas, and Y.C. Kim, Fuzzy irresolute mappings in smooth fuzzy topological spaces, The Journal of Fuzzy Mathematics., 9 (2001) 865-877.
[12] P. Smets, The degree of belief in a fuzzy event, Inform. Sci., 25 (1981) 1-19.
[13] M. Sugeno, An introductory survey of fuzzy control, Inform. Sci., 36 (1985) 59-83.
[14] A.P. Šostak, On a fuzzy topological structure, Rend. Circ. Matem. Palermo Ser II., 11 (1986) 89-103.
[15] A.P. Šostak, On the neighborhood structure of a fuzzy topological spaces, Zh. Rodova Univ. Nis. Ser. Math., 4 (1990) 7-14.
[16] A.P. Šostak, Basic structures of fuzzy topology, J. Math. Sci., 78 (6) (1996) 662-701.
[17] A. Vadivel and E. Elavarasan, Applications of $r$-generalized regular fuzzy closed sets, Annals of Fuzzy Mathematics and Informatics (Accepted).
[18] L.A. Zadeh, Fuzzy sets, Information and control., 8 (1965) 338-353.