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Regular ⍺ Generalized Open Sets In Intuitionistic Fuzzy Topological Spaces

Nivetha M 1, Jayanthi D 2
  1. P.G. Student, Department of Mathematics, Avinashilingam University, Coimbatore, Tamil Nadu, India
  2. Assistant Professor, Department of Mathematics, Avinashilingam University, Coimbatore, Tamil Nadu, India
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Abstract

The purpose of this paper is to introduce and study the concept of intuitionistic fuzzy regular α generalized open sets in intuitionistic fuzzy topological spaces. We investigate some of their properties and also we introduce intuitionistic fuzzy regular α T1/2 space and obtain some characterizations and several preservation theorems.

Keywords
Intuitionistic fuzzy set, Intuitionistic fuzzy topology, Intuitionistic fuzzy topological space, Intuitionistic fuzzy regular α generalized open set, Intuitionistic fuzzy regular α T1/2 space.

INTRODUCTION
The theory of fuzzy sets was introduced by Zadeh [10] in 1965. Later, Chang [2] proposed fuzzy topology in 1967. The concept of intuitionistic fuzzy sets, introduced by Atanassov [1] is a generalization of fuzzy sets. Using the notion of intuitionistic fuzzy sets, Coker [3] introduced the notion of intuitionistic fuzzy topological spaces in 1997.In this paper, we introduce intuitionistic fuzzy regular α generalized open set. We investigate some of their properties. We also introduce intuitionistic fuzzy regular α T1/2 space and obtain some characterizations and several preservation theorems.

II. PRELIMINARIES
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III. INTUITIONISTIC FUZZY REGULAR ⍺ GENERALIZED OPEN SETS
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IV. APPLICATIONS OF INTUITIONISTIC FUZZY REGULAR ⍺ GENERALIZED CLOSED SETS
In this section we provide some applications of intuitionistic fuzzy regular α generalized closed sets. Definition 4.1: If every IFRαGCS in (X,τ) is an IFαCS in (X,τ), then the space can be called as an intuitionistic fuzzy regular α T1/2 space (IFrαT1/2 in short).
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V. CONCLUSION
Thus we have analyzed relationship between intuitionistic fuzzy regular α generalized open sets and the already existing intuitionistic fuzzy open sets and obtain many interesting theorem using the new spaces introduced above.

References
  1. Atanassov, K., “Intuitionistic fuzzy sets”, Fuzzy sets and systems, pp87-96, 1986.
  2. Chang, C.L., “Fuzzy Topological Spaces ”, J.Math. Anal. Appl. 24, pp.182-190, 1968.
  3. Coker, D., “An introduction to intuitionistic fuzzy topological spaces”, Fuzzy sets and systems, pp.81-89, 1997.
  4. Coker, D., and Demirci, M., “On intuitionistic fuzzy points”, Notes on Intuitionistic Fuzzy Sets, 1, 79-84, 1995.
  5. Gurcay, H., Coker, D., and Haydar, Es. A., “On fuzzy continuity in intuitionistic fuzzy topological spaces”, Jour. of Fuzzy Math., 5(2), pp.365-378, 1997
  6. Nivetha, M., and Jayanthi, D., “On Intuitionistic Fuzzy Regular α Generalized closed sets”, International Journal of Engineering Sciences & Research Technology, Vol 4, Issue 2, pp.234-237, 2015 .
  7. Santhi, R., and Jayanthi, D., “Intuitionistic Fuzzy Generalized Semi-Pre Continuous Mappings”, Int. J. Contemp. Math. Science, Vol. 5, no.30, pp.1455 – 1469, 2010.
  8. Santhi, R., and Sakthivel, K., “Alpha generalized homeomorphism in Intuitionistic Fuzzy Topological Spaces”, NIFS 17, 1, pp.30-36, 2011.
  9. Santhi, R., and Sakthivel, K., “Intuitionistic fuzzy almost alpha generalized continuous mapping”, Advances in Fuzzy Mathematics, 2, pp.209-219, 2010.
  10. Zadeh, L.H., “Fuzzy Sets”, Information and Control, 18, pp.338-353, 1965.