Regular and#9082; Generalized Open Sets In Intuitionistic Fuzzy Topological Spaces | Open Access Journals

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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.