ISSN 2348-1218 (print) International Journal of Interdisciplinary Research and Innovations ISSN 2348-1226 (online) Vol. 8, Issue 2, pp: (59-73), Month: April - June 2020, Available at: www.researchpublish.com
INTUITIONISTIC FUZZY G*S-CLOSED SETS Jyoti Pandey Bajpai1, S.S.Thakur2 1
Assistant Professor, 2Professor
Department of Applied Mathematics Jabalpur Engineering College Jabalpur India jyotipbajpai@gmail.com
Abstract: The concept of intuitionistic fuzzy sets was introduced by Atanassov as a generalization of fuzzy sets. In 1997 Coker introduced the concept of intuitionistic fuzzy topological spaces. In 2008, Thakur and Chaturvedi introduced the notion of intuitionistic fuzzy generalized closed set in intuitionistic fuzzy topological space. After that different mathematicians worked and studied in different forms of intuitionistic fuzzy g-closed set and related topological properties. The aim of this paper is to introduce the new class of intuitionistic fuzzy closed sets called intuitionistic fuzzy g*s- closed sets in intuitionistic fuzzy topological space. The class of all intuitionistic fuzzy g*s--closed sets lies between the class of all intuitionistic fuzzy semi-closed sets and class of all intuitionistic fuzzy gspr-closed sets. We also introduce the concepts of intuitionistic fuzzy g*s-- open sets, intuitionistic fuzzy g*s-continuous mappings, intuitionistic fuzzy T*s -space, intuitionistic fuzzy T**s -space and intuitionistic fuzzy * Ts space in intuitionistic fuzzy topological spaces. Keywords: Intuitionistic fuzzy g*s-closed sets, Intuitionistic fuzzy g*s-open sets, Intuitionistic fuzzy g*s continuous mappings, intuitionistic fuzzy T*s -space , and intuitionistic fuzzy T**s –space.
I. INTRODUCTION After the introduction of fuzzy sets by Zadeh [28] in 1965 and fuzzy topology by Chang [7] in 1967, several researches were conducted on the generalizations of the notions of fuzzy sets and fuzzy topology. The concept of intuitionistic fuzzy sets was introduced by Atanassov [1] as a generalization of fuzzy sets. In the last 25 years various concepts of fuzzy mathematics have been extended for intuitionistic fuzzy sets. In 1997 Coker [9] introduced the concept of intuitionistic fuzzy topological spaces. In 2008, Thakur and Chtuvedi [19] introduced the concepts of intuitionistic fuzzy generalized closed sets in intuitionistic fuzzy topology. After that many weak and strong forms of intuitionistic fuzzy g-closed sets such as intuitionistic fuzzy rg-closed sets[20], intuitionistic fuzzy sg-closed sets[21], intuitionistic fuzzy g*-closed sets[8], intuitionistic fuzzy gα-closed sets[13], intuitionistic fuzzy w-closed sets[22], intuitionistic fuzzy rw-closed sets[23], intuitionistic fuzzy gpr-closed sets[24], intuitionistic fuzzy rgα-closed sets[25], intuitionistic fuzzy gsp-closed sets[17], intuitionistic fuzzy gp-closed set[15] , intuitionistic fuzzy strongly g*-closed sets [2], intuitionistic fuzzy sgp-closed sets[3] , ,intuitionistic fuzzy rgw-closed sets[4] and intuitionistic fuzzy g*p-closed sets[5] have been appeared in the literature. In the present paper we introduce the concepts of g*s-closed sets due to Pushpalatha and Anitha K [14] in intuitionistic fuzzy topological spaces. The class of intuitionistic fuzzy g*s-closed sets is properly placed between the class of intuitionistic fuzzy semi closed sets and intuitionistic fuzzy gspr-closed sets. We also introduced the concepts of intuitionistic fuzzy g*s-open sets, and obtain some of their characterization and properties. As an application of this set we introduce intuitionistic fuzzy –T*s-space and intuitionistic fuzzy T**s-space. Further, we introduce intuitionistic fuzzy g*s -continuous mappings with some of its properties.
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