Int. J. Adv. Sci. Eng. Vol.4 No.4 737-739 (2018) 737 ISSN 2349 5359 Satyamurthy V Parvatkar & Sadanand N Patil International Journal of Advanced Science and Engineering www.mahendrapublications.com On Fuzzy strongly g**- closed set in Fuzzy Topological Space Satyamurthy V Parvatkar 1* and Sadanand N Patil 2 1 Department of Mathematics, KLE Institute of Technology, Hubballi, Karnataka - 580030, India 2 Department of Mathematics, Jain Institute of Technology, Davanagere, Karnataka – 577002, India 1. INTRODUCTION In 1965, Zadeh [1] introduced the concept of fuzzy sets. Subsequently many researchers have been worked in this area and related areas which have applications in different field based on this concept. The concept to generalized closed sets plays a significant role in topology. There are many research papers which deal with different types of generalized closed sets. Levine [2] introduced the concept of generalized g*-closed sets (briefly g*-closed) in topological spaces. Chang [3] introduced the concept of fuzzy topological space. g*-closed sets were introduced and studied by Veerakumar [4] for general topology. Recently, Parimelazhagan and Subramonia pillai introduced a strongly g*-closed sets in fuzzy topological space and its various characterization are studied. 2. PRELIMINARIES: Throughout this paper (X,T) represents non-empty fuzzy topological space on which no separation axioms are assumed unless otherwise mentioned. For a subset A of a Space (X,T),cl(A),int(A), and C((X,T)) denote the closure of A, interior of A and the closed sets of (X,T) respectively. Definition 2.1: A subset A of a space (X,T) is called a 1.semi-open set[2] if A ≤ cl(int(A)) and a semi-closed set if int(cl(A)) ≤ A. 2. regular-open set [2] if A=int (cl (A)) and a regular- closed set if int (cl (A))=A. 3.pre-open set[1] if A ≤ int(cl(A)) and pre-closed set if cl(int(A))≤ A. Definition 2.2: A collection U={Vα ,α ∈ A, Vα ∈T} is said to be a proper open cover of the set A in fts (X,T) if and only if for each x∈X there exists Vα x∈ U. Such that uVαxȋxȌ η uA(x),U is countable (finite) proper open cover if A is countable. A subset A of a space (X,T) is called a 1. Regular generalized closed (briefly rg-closed) set [7] if cl(A) ≤ U whenever A ≤ U and U is regular open in (X,T). 2. Generalized closed (briefly g-closed) set [8] if cl(A) ≤ U whenever A ≤ U and U is open in (X,T). 3. Generalized star closed (briefly g*-closed) set [4] if cl (A) ≤ U whenever A ≤ U and U is g-open in (X,T). 4. Generalized star star closed (briefly g**-closed) set [9] if cl(A) ≤ U whenever A ≤ U and U is g*-open in (X,T). 5. Strongly g star closed (briefly strongly g*-closed) set[5] if cl(int(A))≤ U whenever A ≤ U and U is g-open in (X,T). Definition 2.3 A fuzzyset A of (X, T) is called, 1. fuzzy semi open (briefly, f s-openȌ if AζclȋintȋAȌȌ and a fuzzy semi closed(briefly, f s-closedȌ if int[clȋAȌ]ζ A. 2. fuzzy pre open (briefly, f p-openȌif Aζint[clȋAȌ] and a fuzzy pre-closed (briefly, f p-closed) if clȋintȋAȌȌζA. 3. fuzzy α-open (briefly, f α-open Ȍ if A ζ int[clȋintȋAȌȌ] and a fuzzy α-closed (briefly, f α-closed ) if cl(int[clȋAȌ]ȌζA. 4. fuzzy semipre-open (briefly, f sp-open) if Aζcl (int[cl(A)]) and a fuzzy semi pre-closed (briefly, f sp- closed) if int [cl(int(A))] ζA. 5. fuzzy θ-open (briefly, f θ-openȌ if A=intθȋAȌ and a fuzzy θ-closed (briefly, f θ-closed) if A=cl θ (A) where cl(A)=∧{cl(µ): Aζµ, µ∈T}. 6. fuzzy generalized closed(briefly, f g- closed)ifclȋAȌζU,whenever Aζ U and U is fuzzy open set in X. 7. fuzzy generalized semi closed (briefly, g f s- closedȌ if sclȋAȌζ U, whenever Aζ U and U is f s-open set in X. This setisal so called generalized fuzzy weakly semi closed set. 8. fuzzy generalized semi closed (briefly, f gs- closedȌ if sclȋAȌζ U, whenever Aζ U and U is fuzzy open set in X. ABSTRACT: In this paper, we studied the fuzzy topological spaces after giving the fundamental definitions. We have introduced and investigated concept of fuzzy strongly g**-closed set and proved some properties with some examples the way they are related to the sets like fuzzy g*-closed set, fuzzy g**-closed set, pre-closed set, fuzzy strongly g-closed and fuzzy strongly g*-closed set. KEYWORDS: fuzzy strongly g**-closed set. DOI: 10.29294/IJASE.4.4.2018.737-739 © 2018 Mahendrapublications.com, All rights reserved *Corresponding Author: satyaparvatkar@gmail.com Received: 15.02.2018 Accepted: 10.04.2018 Published on: 27.05.2018