Generalized e-closed sets and generalized e-continuity in intuitionistic fuzzy topology

Volume 25, Issue 3, pp 219--231 http://dx.doi.org/10.22436/jmcs.025.03.02

Publication Date: June 16, 2021 Submission Date: February 20, 2021 Revision Date: April 27, 2021 Accteptance Date: May 17, 2021

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Authors

S. S. Thakur - Department of Applied Mathematics, Jabalpur Engineering College, Jabalpur (M.P.) 482011, India. Chandra Prakash Rathor - Department of Mathematics, Rani Durgavati University, Jabalpur (M.P.) 482001, India. Mahima Thakur - Department of Applied Mathematics, Jabalpur Engineering College, Jabalpur (M.P.) 482011, India.

Abstract

The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy generalized e-closed sets and intuitionistic fuzzy generalized e-open sets in intuitionistic Fuzzy topological space. We investigate some of their properties. Further the notion of intuitionistic fuzzy \(_{e} T_{1/2}\) spaces, intuitionistic fuzzy GEO-connectedness, intuitionistic fuzzy GEO-compactness are introduced and studied.

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Keywords

• Intuitionistic fuzzy sets
• intuitionistic fuzzy topology
• intuitionistic fuzzy ge-closed sets and intuitionistic fuzzy ge-continuity

MSC

•  54A40
•  03F55

References

• [1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87--96
  • View Article
  • MathSciNet


• [2] K. Balchandran, P. Sundram, H. Maki, On generalized continuous map in topological spaces, Mem. Fac. Sci. Kochi Univ. Ser. A Math., 12 (1991), 5--13
  • View Article
  • MathSciNet
  • Google Scholar


• [3] V. Chandrasekar, D. Sobana, A. Vadivel, On fuzzy $e$-open sets, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces, Sahand Commun. Math. Anal., 12 (2018), 131--153
  • View Article
  • Google Scholar


• [4] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182--190
  • View Article
  • MathSciNet
  • Google Scholar


• [5] D. Coker, An introduction to intuitionistic fuzzy topological space, Fuzzy Sets and Systems, 88 (1997), 81--89
  • View Article
  • MathSciNet
  • Google Scholar


• [6] D. Coker, A. H. Es, On fuzzy compactness in intuitionistic fuzzy topological spaces, J. Fuzzy Math., 3 (1995), 899--909
  • MathSciNet
  • Google Scholar


• [7] W. Dunham, N. Levine, Further results on generalized closed sets in topology, Kyungpook, Math. J., 20 (1980), 169--175
  • View Article
  • MathSciNet
  • Google Scholar


• [8] H. Gürçay, D. Coker, A. H. Es, On fuzzy continuity in intuitionistic fuzzy topological spaces, J. Fuzzy Math., 5 (1997), 365--378
  • MathSciNet
  • Google Scholar


• [9] I. M. Hanafy, Intuitionistic fuzzy $\gamma$-continuity, Canad. Math. Bull., 52 (2009), 544--554
  • View Article
  • MathSciNet
  • Google Scholar


• [10] E. Hatir, A. Erdogan, Between closed sets and $g$-closed sets, Far East J. Math. Sci. (FJMS), 11 (2003), 289--301
  • MathSciNet
  • Google Scholar


• [11] Y. C. Kim, J. W. Park, Some properties of $r$-generalized fuzzy closed sets, Far East J. Math. Sci. (FJMS), 7 (2002), 253--268
  • MathSciNet
  • Google Scholar


• [12] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo (2), 19 (1970), 89--96
  • View Article
  • MathSciNet
  • Google Scholar


• [13] F. G. Lupiánez, Separation in intuitionistic fuzzy topological spaces, Int. J. Pure Appl. Math., 17 (2004), 29--34
  • View Article
  • MathSciNet
  • Google Scholar


• [14] F. G. Lupiánez, Quasicoincidence for intuitionistic fuzzy points, Int. J. Math. Math. Sci., 2005 (2005), 1539--1542
  • View Article
  • MathSciNet
  • Google Scholar


• [15] F. G. Lupiánez, Nets and filters in intuitionistic fuzzy topological spaces, Inform. Sci., 176 (2006), 2396--2404
  • View Article
  • MathSciNet
  • Google Scholar


• [16] F. G. Lupiánez, Covering properties in intuitionistic fuzzy topological spaces, Kybernetes, 36 (2007), 749--753
  • View Article
  • MathSciNet
  • Google Scholar


• [17] H. Maki, R. Devi, K. Balachandran, Generalized $\alpha$-closed sets in topology, Bull. Fukuoka Univ. Ed. Part III., 42 (1993), 13--21
  • View Article
  • Google Scholar


• [18] H. Maki, R. Devi, K. Balachandran, Associated topologies of generalized $\alpha$-closed sets and $\alpha$-generalized closed set, Mem. Fac. Sci. Kochi Univ. Ser. A Math., 15 (1994), 51--63
  • View Article
  • MathSciNet
  • Google Scholar


• [19] R. Malviya, On certain concepts in fuzzy topology, Ph.D. Dissertation, R. D. V. V. Jabalpur (M.P.) (1997)
  • Google Scholar


• [20] S. S. Thakur, J. P. Bajpai, Intuitionistic fuzzy $sg$-continuous mappings, Int. J. Appl. Math. Anal. Appl., 5 (2010), 45--51
  • View Article


• [21] S. S. Thakur, J. P. Bajpai, Intuitionistic fuzzy $w$-closed sets and intuitionistic fuzzy $w$-continuity, Int. J. Contem. Adv. Math., 1 (2010), 1--15
  • View Article
  • Google Scholar


• [22] S. S. Thakur, J. P. Bajpai, Intuitionistic fuzzy $rg\alpha$-closed sets, International Journal of Fuzzy Systems and Rough Systems, 4 (2011), 67--73
  • Google Scholar


• [23] S. S. Thakur, J. P. Bajpai, Intuitionistic fuzzy $rw$-closed set and intuitionistic fuzzy $rw$-continuity, Notes on Intuitionistic Fuzzy Sets, 17 (2011), 82--96
  • View Article
  • Google Scholar


• [24] S. S. Thakur, J. P. Bajpai, On intuitionistic fuzzy $gpr$-closed sets, Fuzzy Inf. Eng., 4 (2012), 425--444
  • View Article
  • Google Scholar


• [25] S. S. Thakur, R. Chaturvedi, Generalized continuity in intuitionistic fuzzy topological Spaces, Notes on Intuitionistic Fuzzy Sets, 12 (2006), 38--44
  • View Article
  • Google Scholar


• [26] S. S. Thakur, R. Chaturvedi, Intuitionistic fuzzy $rg$-irresolute mappings, Varahmihir J. Math. Sci., 6 (2006), 199--204
  • View Article
  • MathSciNet


• [27] S. S. Thakur, R. Chaturvedi, Regular generalized closed sets in intuitionistic fuzzy topological Spaces, Stud. Cercet. Stiint. Ser. Mat. Univ. Bacau, 16 (2006), 252--272
  • Google Scholar


• [28] S. S. Thakur, R. Chaturvedi, Intuitionistic fuzzy $rg$-continuous mappings, J. Indian Acad. Math., 29 (2007), 467--473
  • MathSciNet


• [29] S. S. Thakur, R. Chaturvedi, Intuitionistic fuzzy $gc$-irresolute mappings, Math. Notae, 45 (2007/08), 59--65
  • MathSciNet


• [30] S. S. Thakur, R. Chaturvedi, Generalized closed sets in intuitionistic fuzzy topology, J. Fuzzy Math., 16 (2008), 559--572
  • MathSciNet
  • Google Scholar


• [31] N. Turnali, D. Coker, Fuzzy connectedness in intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 116 (2000), 369--375
  • View Article
  • MathSciNet
  • Google Scholar


• [32] S. S. Thakur, R. K. Khare, Fuzzy rg-closed mappings, Varahmihir J. Math. Sci., 3 (2003), 65--70
  • Google Scholar


• [33] S. S. Thakur, R. K. Khare, Fuzzy regular generalized continuous mappings, J. Indian Acad. Math., 27 (2005), 355--380
  • MathSciNet


• [34] S. S. Thakur, R. Malviya, Fuzzy $gc$-irresolute mappings, Proc. Math. Soc., 11 (1995), 184--186
  • MathSciNet
  • Google Scholar


• [35] S. S. Thakur, R. Malviya, Generalized closed sets in fuzzy topology, Math. Notae, 38 (1995), 137--140
  • MathSciNet
  • Google Scholar


• [36] L. A. Zadeh, Fuzzy set, Information and Control, 8 (1965), 338--353
  • View Article
  • MathSciNet
  • Google Scholar