Document Type : Research Paper
Authors
- Veerappan Chandrasekar ^{1}
- Durairaj Sobana ^{1}
- Appachi Vadivel ^{} ^{} ^{2}
^{1} Department of Mathematics, Kandaswami Kandar's College, P-velur-638 182, Tamil Nadu, India.
^{2} Department of Mathematics, Annamalai University, Annamalainagar, Tamil Nadu-608 002.
Abstract
The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results related topological concepts. Several preservation properties and some characterizations concerning intuitionistic fuzzy $e$-compactness have been obtained.
Keywords
- Intuitionistic fuzzy set
- Intuitionistic fuzzy point
- Intuitionistic fuzzy topological space
- Intuitionistic fuzzy $e$-open set
- Intuitionistic fuzzy $e$-continuity
- Intuitionistic fuzzy $e$-closure
- Intuitionistic fuzzy $e$-interior
- Intuitionistic fuzzy $e$-compact spaces
Main Subjects
[1] K. Atanassov, Intuitionistic fuzzy sets, VII ITKR's Session, Sofia, 1983, (in Bulgarian).
[2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), pp. 87-96.
[3] C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), pp. 182-190.
[4] D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88 (1997), pp. 81-89.
[5] D. Coker and M. Demirci, On intuitionistic fuzzy points NIFS, 1 (1995), pp. 79-84.
[6] E. Ekici, New forms of contra-continuity, Carpathian J. Math., 24 (2008), pp. 37-45.
[7] E. Ekici, On $e$-open sets, $DP^*$-sets and $DPepsilon^*$-sets and decompositions of continuity, Arab. J. Sci. Eng., 33 (2008), pp. 269-282.
[8] E. Ekici, On $a$-open sets $A^*$-sets and decompositions of continuity and super-continuity, Annales Univ. Sci. Dudapest. Eotvos Sect. Math., 51 (2008), pp. 39-51.
[9] E. Ekici, Some generalizations of almost contra-super-continuity, Filomat, 21 (2007), pp. 31-44.
[10] E. Ekici, On $e^*$-open sets and $(D,S)^*$-sets, Mathematica Moravica, 13 (2009), pp. 29-36.
[11] H. Gurcay, D. Coker, and A.H. Es, On fuzzy continuity in intuitionistic fuzzy topological spaces, J. Fuzzy Math., 5 (1997), pp. 365-378.
[12] V. Seenivasan and K. Kamala, Fuzzy $e$-continuity and fuzzy $e$-open sets, Ann. Fuzzy Math. Inform., 8 (2014), pp. 141-148.
[13] P. Smets, The degree of belief in a fuzzy event, Information Sciences, 25 (1981), pp. 1-19.
[14] M. Sugeno, An introductory survey of fuzzy control, Information Science, 36 (1985), pp. 59-83.
[15] S.S. Thakur and S. Singh, On fuzzy semi-pre open sets and fuzzy semi-pre continuity, Fuzzy Sets and Systems, (1998), pp. 383-391.
[16] L.A. Zadeh, Fuzzy Sets, Inform. and Control, 8 (1965), pp. 338-353.