International Journal of Innovative Research in Science, Engineering and Technology

International Journal of Innovative Research in Science, Engineering and Technology

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Intuitionistic Fuzzy Neutrosophic Soft Topological Spaces

R.Saroja1 and Dr.A.Kalaichelvi2
  1. Research Scholar, Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women,Coimbatore, Tamilnadu, India
  2. Associate Professor, Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, Tamilnadu, India
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Abstract

The aim of this paper is to construct a topology on an intuitionistic fuzzy neutrosophic soft set. The concepts of intuitionistic fuzzy neutrosophic soft closure, intuitionistic fuzzy neutrosophic soft interior, intuitionistic fuzzy neutrosophic soft exterior, intuitionistic fuzzy neutrosophic soft boundary are introduced and some of its properties are studied.

Keywords
Intuitionistic fuzzy neutrosophic soft set,Intuitionistic fuzzy neutrosophic soft topology,Intuitionistic fuzzy neutrosophic soft interior,Intuitionistic fuzzy neutrosophic soft closure,Intuitionistic fuzzy neutrosophic soft exterior, Intuitionistic fuzzy neutrosophic soft boundary.

INTRODUCTION
In 1999, Molodtsov initiated the theory of soft sets as a new mathematical tool for dealing uncertainty. The topological structures of set theory dealing with uncertainties were first studied by Chang in 1968.Chang[4] introduced the notion of fuzzy topology and also studied some of its basic properties. Shabir and Naz[10]introduced the notion of the soft topology and studied some basic concepts such as soft interior, soft closure and soft sub base. Maji, Roy and Biswas [5,6] initiated the concept of fuzzy soft set which is a combination of fuzzy set and soft set. Atanassov[3] defined the concept of intuitionistic fuzzy set which is more general than the fuzzy set and Maji et.al[6] introduced the concept of intuitionistic fuzzy soft set. Smarandache[11] initiated the concept of neutrosophic set and Maji[7] defined the notion of neutrosophic soft set. Arockiarani et.al [1]defined the notion of fuzzy neutrosophic set and fuzzy neutrosophic soft set.

RELATED WORK
Fuzzy soft topological spaces are introduced by TridivJyotiNeog et.al[12].Intuitionistic fuzzy soft topological spaces are introduced by SadiBayramov and Gigdemgunduz[8]. Neutrosophic topological spaces are introduced by Salama and Alblowi[9]. Fuzzy neutrosophic topological spaces and Fuzzy neutrosophic soft topological spaces are introduced by Arockiarani, and MartinaJency[1,2].
In this paper intuitionistic fuzzy neutrosophic soft topological spaces are introduced.Also the concepts of intuitionistic fuzzy neutrosophic soft closure, intuitionistic fuzzy neutrosophic soft interior, intuitionistic fuzzy neutrosophic soft exterior, intuitionistic fuzzy neutrosophic soft boundary are introduced and some important theorems are established.

PRELIMINARIES

DEFINITION:3.1
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INTUITIONISTIC FUZZY NEUTROSOPHIC SOFT TOPOLOGICAL SPACES
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CONCLUSION
In the present work, a new space called intuitionistic fuzzy neutrosophic soft topological space is introduced and some of its properties studied.

References
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  2. Arockiarani, I., Sumathi, I.R., and MartinaJency, J., “ Fuzzy neutrosophic soft topological spaces”,Inter.J.Math.Archive, 4(10),PP.225-238, (2013)
  3. Atanassov, K.T.,“ Intuitionistic fuzzy sets”, fuzzy sets and systems,Vol.20,No.1,PP.87-96,(1986).
  4. Chang, C., “ fuzzy topological spaces”, J.Math.Anal.Appl.,24,PP.182-190,(1968)
  5. Maji, P.K., Roy, A.R., and Biswas, R.,“ Fuzzy soft sets”, J.Fuzzy Math.9(3),PP.589-602, (2001)
  6. Maji , P.K., Roy, A.R., and Biswas, R .,“ Intuitionistic Fuzzy soft sets”, J.FuzzyMath.9(3),PP.677-692,(2001)
  7. Maji, P.K., “Neutrosophic soft set”,Ann.Fuzzy.Math.Inform,Vol.5,No.1,PP.157-168,(2012)
  8. SadiBayramovand Gigdemgunduz., “On intuitionistic fuzzy soft topological spaces”,Inter.J.PureAppl.Math,Vol.5,No.1,PP.66-79,(2014)
  9. Salama, A.A., and Alblowi, S.A., “Neutrosophic set and neutrosophic topological spaces”,IOSRJ.Mathematics,Vol.3,Issue 4,PP.31-35,(2012)
  10. Shabir, M., and Naz, M., “ On soft topological spaces”, Compute.Math.Appl.Vol.6,No.1,PP.1786-1799,(2001)
  11. Smarandache, F.,“Neutrosophic set, A generalization of the intuitionistic fuzzy sets”, Inter.J.Pure Appl.Math,24,PP.289-297,(2005)
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