International Journal for Research in Applied Science & Engineering Technology (IJRASET) ISSN: 2321-9653; IC Value: 45.98; SJ Impact Factor: 7.538 Volume 10 Issue XII Dec 2022- Available at www.ijraset.com IFsgp*-Closed Sets, Open Sets in Intuitionistic Fuzzy Topological Spaces Chandhini. J1, Uma. N2 1 2 Research scholar, Asso Prof. & Head, PG and Research Department of Mathematics, Sri Ramakrishna College of Arts and Science, Coimbatore, Tamil Nadu, India Abstract: In this paper, Intuitionistic fuzzy semi gp* - closed sets, Intuitionistic fuzzy semi gp* - open sets, and characteristics of Intuitionistic fuzzy semi gp* - closed sets are introduced. Here, we have also investigated their relations and properties with other Intuitionistic fuzzy sets. Keywords: Intuitionistic fuzzy topological spaces; Intuitionistic fuzzy gp* - closed set; Intuitionistic fuzzy sgp* - closed sets; Intuitionistic fuzzy sgp* - open sets. I. INTRODUCTION The fuzzy concept was introduced by Zadeh [12] in 1965. Later in 1986, Atanassov [1], presented the Intuitionistic fuzzy sets. In 1997, Coker [3] proposed the Intuitionistic fuzzy topological spaces using Intuitionistic fuzzy sets. Young Bae Jun & Seok Zun Song [11] initiated Intuitionistic fuzzy semi-pre-open sets and Intuitionistic fuzzy semi-pre-continuous mapping in 2005. In 2009, Santhi & Jayanthi [6] [7] defined the concept of Intuitionistic fuzzy generalized semi-pre-closed sets and Intuitionistic fuzzy semipre-continuous mapping. In 2010, Thakur & Jyoti Pandey Bajpai [10] proposed Intuitionistic fuzzy w closed sets and Intuitionistic fuzzy w continuity. In 2010, Shyla Isac Mary & Thangavelu [9] discovered the regular pre-semi-closed sets in topological spaces. Sakthivel [8] founded the Intuitionistic fuzzy alpha generalized closed set and Intuitionistic fuzzy alpha generalized open set in 2012. Ramesh & Thirumalaiswamy [5] in 2019 instituted the generalized semi pre-closed set in Intuitionistic fuzzy topological spaces. In 2016, Jeyaraman, Ravi & Yuvarani [4] proposed the Intuitionistic fuzzy alpha generalized semi-closed set. Chandhini & Uma [2] in 2022 developed the concept of Intuitionistic fuzzy generalized pre-star neighborhood in Intuitionistic fuzzy topological spaces. In this paper, we have defined the new notions of Intuitionistic fuzzy semi-generalized pre-star closed set, Intuitionistic fuzzy generalized pre-star open set in Intuitionistic fuzzy topological spaces and some of their features. Further, we have showed that the IFsgp* of IFTS is productive and have demonstrated some of its features. II. PRELIMINARIES 1) Definition 2.1 [1]: Let be a non-empty fixed set. An Intuitionistic fuzzy set (IFS in short) in X is an object having the form = {< , ( ), ( ) > / ∈ } where the functions ( )∶ → [0, 1] and ( )∶ → [0, 1] denote the degree of membership (namely (x)) and the degree of non - membership (namely ( )) of each element ∈ to a set respectively and 0 ≤ ( ) + ( ) ≤ 1 for each ∈ . 2) Definition 2.2 [1]: Let = {< , ( ), ( ) > / ∈ a) ⊂ if and only if ( ) ≤ ( ) and ( ) ≥ b) = if and only if ⊆ and ⊆ , c) = {< ( ), ( ) > / ∈ }, ( ), ( ) ∪ ( ) >/ d) ∩ = {< , ( ) ∩ ( ), ( ) ∩ ( ) >/ e) ∪ = {< , ( ) ∪ } and = {< , ( ), ( ) for all ∈ , ( ) > / ∈ } be the IFSs, Then }, }. We shall use =< , , > instead ( ), ( ) >} for = {< , ( / , / = {< , ( ( ) ( )), And, 0~ = {< , 0, 1 >/ } is the empty set and 1~ = {< , 1, 0 >/ of = {< , ( ), ( ) >/ } and ), ( / , / )}. } is the whole set of ,the Intuitionistic fuzzy set. ©IJRASET: All Rights are Reserved | SJ Impact Factor 7.538 | ISRA Journal Impact Factor 7.894 | 1271