Separation axioms on fuzzy ideal topological spaces in 𝑺 ̆ ostak‘s sense

Abstract

In the present paper, we introduce the notions of -fuzzy ⋆-open and -fuzzy ⋆-closed sets in Šostak's fuzzy topological spaces. Also, we study some properties of these notions. Moreover, we give the concept of fuzzy ideal ⋆irresolute mapping in Šostak's fuzzy topological spaces. Finally, we study some kinds of separation axioms namely r − FIR where i={0. 1. 2. 3} and r − FIT where j={1. 2. 2 1 2 . 3. 4} and the relations between them. Also, some of their characterizations and several of fundamental properties have been established. Keywords: r-fuzzy ⋆-open r-fuzzy ⋆-closed ℐ ⋆-irresolute mapping r-FIR r-FIT

Single-Valued Neutrosophic Roughness via Ideals

“…Others as Wang et al [4] defined the single-valued neutrosophic set concept. In (2020, 2021) Saber et al [5][6][7][8][9][10][11] introduced and studied the concepts of single-valued neutrosophic ideal, single-valued neutrosophic ideal open local function, connectedness in single-valued neutrosophic topological spaces (£, ˜ σ , ˜ ς , ˜ δ ) and compactness in single-valued neutrosophic ideal topological spaces.…”

Ideals on Generalized Topological Spaces

“…They proved some basic properties for the local closure function, and also introduced two new topologies obtained from the original one using the local closure function. Afterwards, many properties in topological spaces have been explored by various researchers ( [20], [21], [22], [23], [24], [25])…”