Document Type: Research Paper

Authors

1 Young Researchers and Elite Club‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran

2 Department of Mathematics, Khaje Nasir Toosi University of Technology, Tehran, Iran.

3 Department of Mathematics‎, ‎P‎. ‎M‎. ‎Thevar College‎, ‎Usilampatti‎, ‎Madurai Dt‎, ‎Tamil Nadu‎, ‎India

Abstract

‎In this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. Moreover, we study some more properties of this type of closed spaces.

Keywords

Main Subjects

[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] G. Balasubramanian, On fuzzy-pre-separation axiom, Bull., Calcutta Math Soc., 90 (6) (1998) 427--434.

[3] G. Balasubramanian, and V. Chandrasekar, Totally fuzzy semi continuous functions, Bull. Calcutta Mat Soc., 92 (4) (2000) 305--312.

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

[5] S.S. Benchalli and G.P. Siddapur, Fuzzy ${{g}^{*}}$-pre-continuous maps in fuzzy topological spaces, Int. Jou. Comp. Appl., 16 (2) (2011)  12--15.

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

[7] W. Dunham, A new closure operator for non-$T_1$ topologies, Kyungpook Math. J., {22} (1982), 55--60.

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

[9] M. E. El-Shafei and A. Zakari,  $theta $-generalized closed sets in fuzzy topological spaces, The Arabian Journal for Science and Engineering., 31 (2A) (2006) 197--206.

[10] H. Maki, Generalized $Lambda $-sets and the associated closure operator, Special Issue in Commemoration of Prof. Kazusada Ikeda’s Retirement 1. Oct (1986), 139--146.

[11] H.R. Moradi, Bounded and semi bounded inverse theorems in fuzzy normed spaces, International Journal of Fuzzy System Applications., 4 (2) (2015) 47--55.

[12] H.R. Moradi, Characterization of fuzzy complete normed space and fuzzy $b$-complete set, Sahand Communications in Mathematical Analysis., {1} (2) (2014) 65--75.

[13] S. Murugesan and P. Thangavelu, Fuzzy pre-semi-closed sets, Bull. Malays, Math Sci. Soc., 31 (2) (2008) 223--232.

[14] R. Parimelazhagan and V. S. Pillai, Strongly $g$-closed sets in topological spaces, Int. Jou. Of Math. Analy., 6 (30) (2012) 1481--1489.

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

[16] R.K. Saraf, G. Navalagi and M. Khanna, On fuzzy semi-pre-generalized closed sets, Bull.  Malays. Math Sci. Soc., 28 (1) (2005) 19--30.

[17] R.K. Saraf and M. Khanna, On $gs$-closed set in fuzzy topology, J. Indian Acad. Math., 25 (1) (2003) 133--143.

[18] S.S. Thakur and S. Sing, On fuzzy semi-pre open sets and fuzzy semi-pre continuity, Fuzzy Sets and Systems., 98 (3) (1998) 383--391.

[19] M.K.R.S. Veerakumar, Between closed sets and g-closed sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 17 (21) (2000) 1--19.

[20] T.H. Yalvac, Semi-interior and semi-closure of a fuzzy set, J.Math. Anal. Appl., 132 (2) (1988) 356--364.

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