Fuzzy Topological Spaces Research Articles

Nano Fuzzy Z - Open Sets and its Application in Nano Fuzzy Topological Space

This research aims to define and investigate the properties of Nano fuzzy Z-open explicitly sets defined in Nano fuzzy topological spaces. Also, there is an attempt to define Nano fuzzy Z-closure Nano fuzzy Z-interior in Nano fuzzy topological spaces. The work has grown by incorporating Nano fuzzy δ open sets, Nano fuzzy δ semi-open sets, Nano fuzzy δ semi-open sets, and Nano fuzzy δ pre-open sets. Also, the work has been concluded with a numerical application of the Nano fuzzy score function in the medical field (to check the proper diagnosis of disease and drug combinations given to the patient).

Novel Approaches Characterizing Separation in Fuzzy Topology with Quasi-Coincidence

Fuzzy sets were introduced by Zadeh in 1965, and three years later, Chang defined fuzzy topological spaces. Fuzzy topological spaces are families of fuzzy sets that satisfy the three classical axioms of topology. In this paper, we introduce and study some new notions of To separation axioms in fuzzy topological spaces using the quasi-coincident relation for fuzzy sets. Every ordinary (crisp) topological space vacuously satisfies the condition of being quasi-To. We define the quasi-separation axioms for fuzzy topological spaces, as quasi-To, quasi-T1, Quasi-T2. We have introduced and studied some new notions of To separation axioms in fuzzy topological spaces using the quasi-coincident relation for fuzzy sets. These quasi-separation axioms are weaker than the corresponding classical To separation axioms, but they are still useful for characterizing and studying fuzzy topological spaces.

ON ALMOST CONTRA-SOMEWHAT FUZZY CONTINUOUS FUNCTIONS

In this paper, a new notion of fuzzy contra-continuity, called almost contra-somewhat fuzzy continuity between fuzzy topological spaces,is introduced. Several characterizations of these functions are obtained and it is shown that fuzzy almost contra-semi continuous functions are almost contra-somewhat fuzzy continuous functions. The conditions under which fuzzy hyper connected spaces become the fuzzy Baire spaces, fuzzy second category spaces and fuzzy almost irresolvable spaces, are obtained by means of almost contra-somewhat fuzzy continuous functions.

The βm – Homeomorphism in Double Fuzzy Topological Spaces

The purpose of this study is to introduce the concept of homeomorphism via βm – closed set and study its behavior and properties in double fuzzy topological spaces. This objective is achieved through the definitions of df- βm continuous functions and df- βm closed functions. The results of this study represent important relationships and proofs, in addition to providing some necessary examples.

Applications of intuitionistic fuzzy sets to assessment, decision making and to topological spaces

The intuitionistic fuzzy sets, in which the elements of the universe have their membership and non-membership degrees in [0, 1], are a generalization of Zadeh’s fuzzy set. In this paper, intuitionistic fuzzy sets are used as tools for assessment and decision-making. This is useful in cases where one is not sure about the suitability of the linguistic characterizations assigned to each element of the universal set. Further, it is described how the notions of convergence, continuity, compactness, and of Hausdorff topological space are extended to intuitionistic fuzzy topological spaces. Applications illustrating our results are also presented.

Characterizations of generalized Fuzzy γ∗-closed sets

Generalized fuzzy open sets are playing a vital role in the study of fuzzy topological space as well as that of fuzzy bitopological space since its inception. More often, it is reported that fuzzy closed sets are always included in the family of generalized fuzzy closed sets. Very recently, it has appeared that fuzzy γ∗ -open sets are incomparable with fuzzy open sets. This paper aims to present three different kinds of fuzzy generalized closed sets in the light of fuzzy γ∗ -open set and associated closure operators with the terminologies- generalized fuzzy γ∗ -closed set, γ∗ -generalized fuzzy closed set and γ∗ -generalized fuzzy γ∗-closed set and it is found that the relation between any two concepts is not necessarily linear. Also, the interrelationships among them are established along with suitable counter examples which are properly placed to make the paper self-sufficient.

Mixed Fuzzy topological space its Hausdorff properties and base

In this article, mixed fuzzy topology and its topological properties have been studied. Mixed fuzzy topology is defined with the help of quasi-coincidence and closure of a fuzzy set in one of the fuzzy topologies. Thus, a new fuzzy topology is generated from the given two fuzzy topologies. This new fuzzy topology may or may not contain the topological properties of the parent topologies. This study identifies some topological properties that are carried to the mixed fuzzy topology from the given parent fuzzy topologies and some other properties which are not carried to the mixed fuzzy topology. Here a base for mixed fuzzy topology from the bases of the given parent topologies is constructed. Considering the regularity of one of the parent topologies mixed fuzzy topology is investigated. Hausdorff’s properties of mixed fuzzy topological spaces are also discussed. It is now of general interest to know which properties are carried to the mixed topology and which are not. A few of these are being tried to answer here in this paper.

On Some New Forms of Fsgb-Continuous Mappings in Fuzzy Topological Spaces.

On Some New Forms of Fsgb-Continuous Mappings in Fuzzy Topological Spaces.

Weaker Form of Fuzzy Minimal Open Sets and a Stronger Form of Fuzzy Mean Open Sets

In a fuzzy topological space, this article introduces fuzzy locally minimal open, fuzzy s-mean open sets at certain fuzzy points. Additionally, several of those fuzzy open sets attributes are expanded. Fuzzy mean open sets are weaker than the fuzzy s-mean open. We note that for each of its fuzzy points, a fuzzy minimum open is a fuzzy locally minimal open set.

FUZZY TOPOLOGICAL MODULES INDUCED BY FUZZY PSEUDO NORMED MODULE

In this article, we give defines about fuzzy pseudo norm module space and fuzzy metric module space which induces by this space. Complete metric space was proved. Also we are defining fuzzy topological module space which induces by fuzzy metric module space.

FUZZY TOPOLOGICAL MODULES INDUCED BY FUZZY PSEUDO NORMED MODULE

In this article, we give defines about fuzzy pseudo norm module space and fuzzy metric module space which induces by this space. Complete metric space was proved. Also we are defining fuzzy topological module space which induces by fuzzy metric module space.

Fuzzy wg**- Connectedness in Fuzzy Topological Spaces

Fuzzy wg**- Connectedness in Fuzzy Topological Spaces

INTUITIONISTIC FUZZY SUPRA CONTRA SEMI-HOMEOMORPHISM

The aim of the present paper is to introduce two classes of open mappings using intuitionistic fuzzy supra open sets and semi-supra open sets in intuitionistic fuzzy supra topological spaces. It is nothing but, the image of intuitionistic fuzzy supra open set (resp. supra open) is intuitionistic fuzzy semi-supra closed set (resp. supra closed) in co-domain space. Moreover , a few of their significant properties have been studied. A necessary and sufficient condition for intuitionistic fuzzy supra contra semi-open mapping has been derived in terms of semi-supra closure and semi-supra interior. Also, the class of intuitionistic fuzzy supra contra open mappings is properly contained in that of intuitionistic fuzzy supra contra semi-open mappings has been investigated. Suitable examples have been given to establish that the reversible implications are lacking in general. A notion of intuitionistic fuzzy supra contra semi-homeomorphism has been defined and characterized.

Fuzzy g ̃-Continuous Functions and Fuzzy g ̃-Irresolute Continuous Functions in Fuzzy Topological Spaces

In present of this paper, new classes of generalized fuzzy continuous functions called fuzzy -continuous functions and fuzzy -irresolute continuous functions are defined and studied. Also, several examples are given.

On Fuzzy Point Applications of Fuzzy Topological Spaces

On Fuzzy Point Applications of Fuzzy Topological Spaces

Study on Fuzzy β- Supercontinuous Function in Fuzzy Topological Spaces

The main aim of this research is introducing and characterizing new concepts of fuzzy continuity using the definition of fuzzy β-sets and fuzzy βs -sets including fuzzy - supercontinuous. some of their basic properties are examined. After that some theorem by using these properties have been proved.

Decision-making to limit epidemics spread based on fuzzy-soft and topological spaces

Real-world applications process enormous amounts of data, especially in the area of large-dimension features. This work aims to present new classes of functions based on SM*-open sets that are a modification of simply open sets; namely, SM*-continuous, SM*-irresolute, proper continuous, SM*-open, SM*-closed, strongly SM*-irresolute, Pre SM*-irresolute, Pre SM*-open, super SM*-open and completely irresolute. The idea of fuzzy soft multifunction between fuzzy soft topological spaces, developed by Metin, is frequently used. Our current research project uses our suggested idea to introduce coronavirus application and infer the most important causal symptoms of coronavirus patients. Furthermore, we created an algorithm to demonstrate the applicability of our proposed technique based on the presented concept. Additionally, the results obtained using MATLAB programming. Finally, realistic WHO-compliant results were achieved for the most serious symptoms of coronavirus patients, as well as a suggested strategy that is competitive. Therefore, decision-making in the future needs to consider our suggestion. In order to promote the long-term wellbeing of both nature and humanity. Our proposed approach is reasonable and effective. The results showed that the methodology we used was reliable as it was consistent with World Health Organization publications.

Ifgp Continuous Mapping, Ifgp Irresolute Mapping, and Ifgp Connectedness in Intuitionistic Fuzzy Topological Spaces

Ifgp Continuous Mapping, Ifgp Irresolute Mapping, and Ifgp Connectedness in Intuitionistic Fuzzy Topological Spaces

On Fuzzy Pre-Λ-Sets and Fuzzy Semi-Λ- Sets

This paper is devoted to study the notions of fuzzy pre-Λ-set, fuzzy semi-Λ- set, fuzzy pre- V -set and fuzzy semi- V - set in fuzzy topological space. We study some properties and discuss the relationships between fuzzy pre-Λ-set, fuzzy semi-Λ- set, fuzzy pre- V -set and fuzzy semi- V - set and relevant concepts in fuzzy topological spaces and to investigate some basic yet essential properties.

On α-Fuzzy Soft Irreducible Spaces

We define fuzzy soft irreducible sets, a-fuzzy soft irreducible sets in fuzzy soft topological spaces and study the properties including (fuzzy soft continuity; fuzzy soft homeomorphism and fuzzy soft topological properties) on a-fuzzy soft irreducible sets.