Fuzzy almost generalized $e$-continuous mappings

Subject Areas : History and biography

A. Vadivel ¹ , B. Vijayalakshmi ²

1 - Department of Mathematics, Annamalai University, Annamalai Nagar, Chidambaram, India
2 - Department of Mathematics, Annamalai University, Annamalai Nagar, Chidambaram, India

Received: 2017-03-09 Accepted : 2017-12-15 Published : 2017-12-10

Keywords: Fuzzy almost generalized $e$-continuous, $fge$-space, $fge$-regular space, $f T_{frac{1}{2}}e$-space,

Abstract :

In this paper, we introduce and characterize the concept of fuzzy almost generalized $e$-continuous mappings. Several interesting properties of these mappings are also given. Examples and counter examples are also given to illustrate the concepts introduced in the paper. We also introduce the concept of fuzzy $f T_{\frac{1}{2}}e$-space, fuzzy $ge$-space, fuzzy regular $ge$-space and fuzzy generalized $e$-compact space. It is seen that a fuzzy almost generalized $e$-continuous mapping from a fuzzy $f T_{\frac{1}{2}}e$-space to another fuzzy topological space becomes fuzzy almost continuous mapping.

References:

[1] K. K. Azad, On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl. 82 (1) (1981), 14-32.

[2] K. Balachandran, P. Sundaram, H. Maki, On generalized continuous maps in topological spaces, Mem. Fac. Sci. Kochi Univ (Math). 12 (1991), 5-13.

[3] A. S. Bin Shahna, On fuzzy strong continuity and fuzzy precontinuity, Fuzzy Sets and Systems. 44 (1991), 303-308.

[4] R. N. Bhaumik, Anjan Mukherjee, Fuzzy completely continuous mappings, Fuzzy Sets and Systems. 56 (1993), 243-246.

[5] G. Balasubramanian, P. Sundaram, On some generalizations of fuzzy continuous functions, Fuzzy Sets and Systems, 86 (1) (1997), 93-100.

[6] G. Balasubramanian, P. Sundaram, On Fuzzy β-T1 spaces and its generalizations, Bull. Cal. Math. Soc. 94 2 (6) (2002), 413-420.

[7] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl. 24 (1968), 182-190.

[8] W. Dunham, N. Levine, Further results on generalized closed sets in topology, Kyungpook Math. J. 20 (1980), 169-175.

[9] W. Dunham, A new closure operator for non-T1 topologies, Kyungpook Math. J. 22 (1982), 55-60.

[10] E. Ekici, On e-open sets, DP ∗-sets and DP ϵ∗-sets and decompositions of continuity, Arab. J. for Sci. and Engin. 33 (2A) (2008), 269-282.

[11] E. Ekici, Some generalizations of almost contra-super-continuity, Filomat, 21 (2) (2007), 31-44.

[12] E. Ekici, New forms of contra-continuity, Carpathian Journal of Mathematics. 24 (1) (2008), 37-45.

[13] E. Ekici, On e∗-open sets and (D, S)∗-sets, Mathematica Moravica. 13 (1) (2009), 29-36.

[14] E. Ekici, On a-open sets A∗-sets and decompositions of continuity and super-continuity, Annales Univ. Sci. Dudapest. Eotvos Sect. Math. 51 (2008), 39-51.

[15] S. Ganguly, S. Saha, A note on δ-continuity and δ-connected sets in fuzzy settings, Simon Stevin, 62 (2) (1988), 127-141.

[16] S. Ganguly, S. Saha, A note on compactness in fuzzy setting, Fuzzy Sets and Systems. 34 (1990), 117-124.

[17] J. K. Kohli, A. R. Prasannan, Pseudu fuzzy continuous maps and pseudo fuzzy homeomorphism, Bull. Cal. Math. Soc. 93 (2) (2001), 69-76.

[18] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo. 19 (2) (1970), 89-96.

[19] M. N. Mukherjee, B. Ghosh, On fuzzy S-closed spaces and FSC sets, Bull. Malaysian Math. Soc. 12 (1989), 1-14.

[20] A. Mukherjee, P. K. Deb, On fuzzy almost semi -pre continuous mappings, Proc. Nat. Sem. On Rec. Dev. In Math. And its Appl. (2008), 147-154.

[21] P.-M. Pu, Y.-M. Liu, Fuzzy topology I: Neighborhood structure of a fuzzy point and Moore smith convergence, J. Math. Anal. Appl. 76 (2) (1980), 571-599.

[22] N. Palaniappan, K. C. Rao, Regular generalized closed sets, kyungpook Math. 33 (2) (1993), 211-219.

[23] J. H. Park, B. H. Park, Fuzzy Pre-irresolute mappings, Pusan Kyongnam Math. J. 10 (1994), 303-312.

[24] P. Smets, The degree of belief in a fuzzy event, Information Sciences. 25 (1) (1981) 1-19.

[25] M. Sugeno, An introductory survey of fuzzy control, Information Sciences. 36 (1-2) (1985) 59-83.

[26] EL. M. E. Shafei, A. Zakari, Semi-generalized continuous mappings in fuzzy topological spaces, The journal of Fuzzy Math. 15 (1) (2007), 109-120.

[27] V. Seenivasan, K. Kamala, Fuzzy e-continuity and fuzzy e-open sets, Ann. Fuzzy Math. Inform. 8 (1) (2014), 141-148.

[28] V. Seenivasan, K. Kamala, Some aspects of fuzzy ~e-closed set, Ann. Fuzzy Math. Inform. 9 (6) (2015), 1019-1027.

[29] V. Seenivasan, K. Kamala, e-Compact Spaces in Fuzzy Topological Spaces, Proceedings of the International Conference on Mathematics and its Applications. (2014), 15-17.

[30] S. S. Thakur, P. K. Khare, Fuzzy semi -pre open, Fuzzy semi -pre continuous mappings, stud. Cerc. St. Ser. Mat. Univ. Bacau, 2004.

[31] N. Velico, H-closed topological spaces, Amer. Math. Soc. Transl. 78 (2) (1968), 103-118.

[32] L. A. Zadeh, Fuzzy sets, Information and Control. 8 (1965), 338-353.