On r -Generalized Fuzzy ℓ -Closed Sets: Properties and Applications

In the present study, we introduce and characterize the class of r -generalized fuzzy ℓ -closed sets in a fuzzy ideal topological space X , τ , ℓ in Šostak sense. Also, we show that r -generalized fuzzy closed set by Kim and Park (2002) ⟹ r -generalized fuzzy ℓ -closed set, but the converse need not be true. Moreover, if we take ℓ = ℓ 0 , the r -generalized fuzzy ℓ -closed set and r -generalized fuzzy closed set are equivalent. After that, we define fuzzy upper (lower) generalized ℓ -continuous multifunctions, and some properties of these multifunctions along with their mutual relationships are studied with the help of examples. Finally, some separation axioms of r -generalized fuzzy ℓ -closed sets are introduced and studied. Also, the notion of r -fuzzy G ∗ -connected sets is defined and studied with help of r -generalized fuzzy ℓ -closed sets.

An Absolutely New Attempt to Vague Soft Bitopological Spaces Basis at Newly Defined Operations regarding Vague Soft Points

In this study, new operations of union, intersection, and complement are defined with the help of vague soft sets in a new way that is in both true and false statements, union is defined with maximum, and intersection is defined with minimum. On the basis of these operations, vague soft topology is defined. Pairwise vague soft open sets and pairwise vague soft closed sets are defined in vague soft bitopological structures (VSBTS). Moreover, generalized vague soft open sets are introduced in VSBTS concerning soft points of the space. On the basis of generalized vague soft open sets, separation axioms are also introduced. In continuation, these separations axioms are engaged with other important results in VSBTS.

On generalized γµ-closed sets and related continuity

In this paper our main interest is to introduce a new type of generalized open sets defined in terms of an operation on a generalized topological space. We have studied some properties of this newly defined sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have studied some preservation theorems in terms of some irresolute functions.

A new approach to vague soft toplogical structures concerning soft points

This paper concerns the study of the notion of vague soft β-open set and vague soft separation axioms in vague soft topological spaces. By using such notions and that of the vague soft pints, we study the separation axioms βi (with i = 0, 1, 2, 3, 4) in vague soft topological spaces. We give some peculiar examples about them and we prove some relationships between them. The relationship of βi (with i = , 1, 2, 3, 4) spaces with the closer of vague soft β-open set by means of soft points, vague soft countable spaces and their relationship with βi (with i = , 1, 2) spaces by means of soft points are addressed. In continuation, vague soft topological, vague soft inverse topological spaces properties, Bolzano Weirstrass Property(BVP) and its topological characteristics, compact spaces and sequentially compact spaces and their relationship with separation axioms by means soft points are addressed in vague soft topological spaces.

Two Classes of Infrasoft Separation Axioms

One of the considerable topics in the soft setting is the study of soft topology which has enticed the attention of many researchers. To contribute to this scope, we devote this work to investigate two classes of separation axioms with respect to the distinct ordinary elements through one of the generalizations of soft topology called infrasoft topology. We first formulate the concepts of infra- t p -soft T j using total belong and partial nonbelong relations and then introduce the concepts of infra- t t -soft T j -spaces using total belong and partial nonbelong relations. To illustrate the relationships between them, we provide some examples. We discuss their fundamental properties and study their behaviors under some special types of infrasoft topologies. An extensive discussion is given for the transmission of these two classes between infrasoft topology and its parametric infratopologies. In the end, we demonstrate which ones have topological and hereditary properties, and we show their behaviors under the finite product of soft spaces.

Soft e-Separation Axioms in Neutrosophic soft Topological Spaces

In this paper, the idea of neutrosophic soft e-neighbourhood and neutrosophic soft e-separation axioms in neutrosophic soft topological spaces are introduces. Later, we discussed about the concept of neutrosophic soft e-separation axioms of neutrosophic soft topological spaces is diffused in different results with respect to neutrosophic soft points. Furthermore, we discuss the properties of neutrosophic soft e-Ti-spaces (i = 0,1, 2, 3,4) and the relations between them.

Intuitionistic Fuzzy Supra Bitopological Spaces

In this paper we will introduce the concept of intuitionistic fuzzy supra bitopological spaces and study the fundamental properties of intuitionistic fuzzy supra bitopological spaces. Also introduce intuitionistic fuzzy supra bi-continuous functions in intuitionistic fuzzy supra bitopological spaces. Moreover introduce the concept of intuitionistic fuzzy supra pairwise separation axioms namely intuitionistic fuzzy supra pairwise Ti where i 2 f0; 1; 2; 3; 4g of intuitionistic fuzzy supra bitopological spaces.

Properties and Applications of d*g? - Closed Sets in Topological Spaces

We introduce the concept of d*g?-closed sets in a topological space and investigate their properties. Moreover, we investigate new separation axioms and new functions in topological spaces.