Fuzzy Soft Topological Spaces Research Articles

Fuzzy Soft Generalized Closed Sets in Fuzzy Soft Topological Spaces

Fuzzy Soft Generalized Closed Sets in Fuzzy Soft Topological Spaces

Connectedness in C ̌ech Fuzzy Soft Closure Spaces

The notion of ech fuzzy soft closure spaces was defined and its basic properties are introduced very newly by Majeed [1]. In the present paper, we define the notion of fuzzy soft separated sets in ech fuzzy soft closure spaces and prove some properties concerning to this notion. By using the notion of fuzzy soft separated sets we introduce and study the concept of connected in both ech fuzzy soft closure spaces and their associative fuzzy soft topological spaces. Then we introduce the concept of feebly connected, and discuss the relationship between the concepts of connected and feebly connected. Finally, we introduce several examples to clarify our results.

A New Class of Continuous Functions in Fuzzy Soft Topological Spaces

A New Class of Continuous Functions in Fuzzy Soft Topological Spaces

Connectedness in Fuzzy Soft Topological Spaces

In this paper, we define the fuzzy soft operator $$\;\phi \;$$ constructed from a fuzzy soft grill $$\;\mathcal {G}_{_{E}}\;$$ and a fuzzy soft topological space $$(X, \tau _{_{E}}).$$ Also, we introduce and study the notion of connectedness to fuzzy soft topological spaces with fuzzy soft grills. Furthermore, we extend the notion of $$\alpha $$ -connectedness related to a fuzzy soft operator $$\;\alpha \;$$ on the set X.

σ-Algebra and σ-Baire in Fuzzy Soft Setting

We first introduce some new notions of Baireness in fuzzy soft topological space (FSTS). Next, their characterizations and basic properties are investigated in this work. The notions of fuzzy soft dense, fuzzy soft nowhere dense, fuzzy soft meager, fuzzy soft second category, fuzzy soft residual, fuzzy soft Baire, fuzzy soft δ-sets, fuzzy soft λσ-sets, fuzzy soft σ-nowhere dense, fuzzy soft σ-meager, fuzzy soft σ-residual, fuzzy soft σ-Baire, fuzzy soft σ-second category, fuzzy soft σ-residual, fuzzy, fuzzy soft submaximal space, fuzzy soft P-space, fuzzy soft almost resolvable space, fuzzy soft hyperconnected space, fuzzy soft A-embedded, fuzzy soft D-Baire, fuzzy soft almost P-spaces, fuzzy soft Borel, and fuzzy soft σ-algebra are introduced. Furthermore, several examples are shown as well.

Some Properties of Fuzzy Soft B-Open Sets and Fuzzy Soft B-Continuous Functions in Fuzzy Soft Topological Spaces

Some Properties of Fuzzy Soft B-Open Sets and Fuzzy Soft B-Continuous Functions in Fuzzy Soft Topological Spaces

Generalized Fuzzy Soft Connected Sets in Generalized Fuzzy Soft Topological Spaces

In this paper we introduce some types of generalized fuzzy soft separated sets and study some of their properties. Next, the notion of connectedness in fuzzy soft topological spaces due to Karata et al, Mahanta et al, and Kandil et al., extended to generalized fuzzy soft topological spaces. The relationship between these types of connectedness in generalized fuzzy soft topological spaces is investigated with the help of number of counter examples.

C̆ech Fuzzy Soft Closure Spaces

In this paper, the C̆ech fuzzy soft closure spaces are defined and their basic properties are studied. Closed (respectively, open) fuzzy soft sets is defined in C̆ech fuzzy-soft closure spaces. It has been shown that for each C̆ech fuzzy soft closure space there is an associated fuzzy soft topological space. In addition, the concepts of a subspace and a sum are defined in C̆ech fuzzy soft closure space. Finally, fuzzy soft continuous (respectively, open and closed) mapping between C̆ech fuzzy soft closure spaces are introduced. Mathematics Subject Classification: 54A40, 54B05, 54C05.

Fuzzy soft filter convergence

In this paper, we introduce the concept of fuzzy soft filters and study some of their properties. Also, we study the notion of convergence of fuzzy soft filters in fuzzy soft topological spaces. We prove the existence of product fuzzy soft filters.

Relationship Between Fuzzy Soft Topological Spaces and Parameter Spaces

In this paper, the relation between fuzzy soft topological spaces and parameter spaces is introduced. After defining the parametrical property of fuzzy soft sets and we give some examples.

Fuzzy soft connected sets in fuzzy soft topological spaces II

Abstract In this paper, we introduce some different types of fuzzy soft connected components related to the different types of fuzzy soft connectedness and based on an equivalence relation defined on the set of fuzzy soft points of X. We have investigated some very interesting properties for fuzzy soft connected components. We show that the fuzzy soft C5-connected component may be not exists and if it exists, it may not be fuzzy soft closed set. Also, we introduced some very interesting properties for fuzzy soft connected components in discrete fuzzy soft topological spaces which is a departure from the general topology.

On Fuzzy Rough Compactness

The notion of rough topological space has been well defined and studied by a number of researchers. Connectedness and compactness of fuzzy soft topological spaces have also been studied by some authors. In this paper we introduce the notion of compactness in fuzzy rough sets and establish some interesting theorems.

On Fuzzy Soft Semi-Pre-Open Sets and Fuzzy Soft Semi-Pre-Continuous Mappings

The main aim of this paper is to initiate and explore the properties of fuzzy soft semi-pre-open(closed) sets. We introduce and investigate fuzzy soft semi-pre-interior and fuzzy soft semi-pre-closure in fuzzy soft topological spaces. Moreover, we dene and study the characterizations of fuzzy soft semi-pre-continuous and fuzzy soft semi-pre-open(closed) mappings in fuzzy soft topological spaces.

On Weak and Strong Forms of Fuzzy Soft Open Sets

We introduce and examined some basic properties of fuzzy soft α-open (closed) sets in fuzzy soft topological spaces. Fuzzy soft pre-open (closed) sets are also defined and discussed. We also initiate and explore fuzzy soft neighborhood at fuzzy soft point. Some properties of fuzzy soft neighborhood system, fuzzy soft basic neighborhood and fuzzy soft neighborhood (nbd) base at fuzzy soft point are studied. Moreover, we define and study fuzzy soft regular open (closed) sets. We analyze the relationship between these notions by providing examples and counter examples.

Fuzzy Soft Connected Sets in Fuzzy Soft Topological Spaces

In this paper we introduce some types of fuzzy soft separated sets and study some of thier preperties. Next, the notion of connectedness in fuzzy topological spaces due to Ming and Ming, Zheng etc., extended to fuzzy soft topological spaces. The relationship between these types of connectedness in fuzzy soft topological spaces is investigated with the help of number of counter examples.

CATS of soft topological spaces

The goal of this study is to consider the natural interrelations between all of the (fuzzy) soft topological spaces in the categorical viewpoint. For this reason, the categories of (fuzzy) soft topological spaces are constructed and then the relations between these categories are observed by using the defined functors.

Fuzzy Soft Compact Topological Spaces

In this paper, we have studied compactness in fuzzy soft topological spaces which is a generalization of the corresponding concept by R. Lowen in the case of fuzzy topological spaces. Several basic desirable results have been established. In particular, we have proved the counterparts of Alexander’s subbase lemma and Tychonoff theorem for fuzzy soft topological spaces.

Fuzzy Soft α-Connectedness in Fuzzy Soft Topological Spaces

In the present paper, we study and investigate the properties of fuzzy soft α-connected sets, fuzzy soft α-separated sets and fuzzy soft α-s-connected sets and establish several interesting propert ies supported by examples. Moreover, we show that, a fuzzy soft α-disconnectedness is not an hereditary property in general. Finally, we show that the fuzzy α-irresolute surjective soft image of fuzzy soft α-connected (resp. fuzzy soft α-s-connected) is also fuzzy soft α-connected (resp. fuzzy soft α-s-connected).

English

In this paper, union, and intersection of generalised fuzzy soft sets are introduced and some of their basic properties are studied. The objective of this paper is to introduce the generalised fuzzy soft topology over a soft universe with a fixed set of parameters. Generalised fuzzy soft points, generalised fuzzy soft closure, generalised fuzzy soft neighbourhood, generalised fuzzy soft interior, generalised fuzzy soft base are introduced and their basic properties are investigated. Finally, generalised fuzzy soft compact spaces are introduced and a few basic properties are taken up for consideration.   Key words: Fuzzy soft set, generalised fuzzy soft set, generalised fuzzy soft topology, generalised fuzzy soft open sets, generalised fuzzy soft closed sets, generalised fuzzy soft topological spaces, generalised fuzzy soft compact spaces.

An Introduction to Fuzzy Soft Topological Spaces

The aim of this study is to dene fuzzy soft topology which will be compatible to the fuzzy soft theory and investigate some of its fundamental properties. Firstly, we recall some basic properties of fuzzy soft sets and then we give the denitions of cartesian product of two fuzzy soft sets and projection mappings. Secondly, we introduce fuzzy soft topology and fuzzy soft continuous mapping. Moreover, we induce a fuzzy soft topology after given the denition of a fuzzy soft base. Also, we obtain an initial fuzzy soft topology and give the denition of product fuzzy soft topology. Finally, we prove that the category of fuzzy soft topological spaces FSTOP is a topological category over SET: