On (r, s)-connectedness in intuitionistic fuzzy topological spaces

Abstract

The aim of this paper is to establish the (r, s)-connectedness in intuitionistic fuzzy topological space. Here we give two new notions of (r, s)-connectedness and total (r, s)-connectedness in intuitionistic fuzzy topological space. Also, we find a relation about classical topology and intuitionistic fuzzy topology. Furthermore, using some provisos we will show that (r, s)-connectedness in intuitionistic fuzzy topological spaces are productive and some of its features.

T_0 Separation Axioms in Intuitionistic Topological Spaces

“…Islam (Islam et al, 2018b) studied intuitionistic spaces, and Islam (Islam et al, 2018a) studied level separation on intuitionistic fuzzy spaces. Mahbub (Mahbub et al, 2019(Mahbub et al, , 2021(Mahbub et al, , 2022 studied a particular type of connectedness and compactness in intuitionistic fuzzy topological spaces.…”

Remark on Intuitionistic Fuzzy Temporal Modal Topological Structures

“…As mentioned in [6], the first time the concept of a "temporal topology" was used was probably in Robin Le Poidevin's paper [7], while the concept of a temporal intuitionistic fuzzy topology in Šostak's sense was discussed by Fatih Kutlu and Tunay Bilgin in [8][9][10]. Other results in the area of intuitionistic fuzzy topology are described in [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. More precisely, in [11], a standard IF-topological structure was described for the first time; in [12][13][14][15]20,24,25], some types of IF-topological spaces were discussed; and in [16,17,19,21,26], some properties of these spaces (e.g., compactness, connectedness, and others) were studied.…”

“…Other results in the area of intuitionistic fuzzy topology are described in [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. More precisely, in [11], a standard IF-topological structure was described for the first time; in [12][13][14][15]20,24,25], some types of IF-topological spaces were discussed; and in [16,17,19,21,26], some properties of these spaces (e.g., compactness, connectedness, and others) were studied. The category of IF-topological space was further introduced in [18], with the properties of the mappings over IF topological spaces elaborated in [22,23] and IF-metric spaces introduced in [27].…”