Fuzzy Topology Research Articles

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.

Application of Intuitionistic Fuzzy Topological Operators in Spatial Objects Modeling

The concept of topology is widely used in mathematical modeling of spatial objects and in GIS. One such application of fuzzy topological operators, detecting areas affected by Mikania micrantha, was studied by Shi and Liu. The precision of the results was evaluated by applying the intuitionistic fuzzy pre-interior and pre-clouser operators defined by the author to the data included in this study.
 With this application example, it has been shown that the newly defined operators give results closer to the real bounds.

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

Intuitionistic Fuzzy Soft Topology via Neighborhood

In this paper, we bring out some properties of intuitionistic fuzzy soft topology by using the concept of neighborhood. Firstly, we introduce the concept of intuitionistic fuzzy soft point differently from the previous published papers which is related to intuitonistic fuzzy soft point and study some of its basic properties. We also generate an intuitonistic fuzzy soft topology by using the systems of neighborhood and discuss certain properties of intuitonistic fuzzy soft topology including continuous mapping.

Regular Open Sets on The Intuitionistic Fuzzy Topological Spaces in Sostak's Sense

The aim of this paper is to introduce and study the concepts of intuitionistic r-fuzzy regular open sets and their related notions in topological spaces.

A New Notion of Paranorm Intuitionistic Fuzzy Zweier I<sub>3</sub>-Convergent Triple Sequence Spaces

In this paper, we define and introduce the notion of paranorm intuitionistic fuzzy Zweier I3-convergent triple sequence spaces ZI3(μ,υ) (p) and ZIO3(μ,υ) (p) for p = (pnmj ) a triple sequence of positive real numbers. Besides, the fuzzy topology on these spaces is studied.

An adaptive fuzzy logic control technique for LVRT enhancement of a grid-integrated DFIG-based wind energy conversion system

The fast improvement of wind energy conversion technology with optimization algorithms has recently received a lot of attention. However, their slow convergence speed, huge computational load, and low efficiency are the main drawbacks and to improve these disadvantages, a new adaptive fuzzy logic controller strategy is proposed to enhance the low voltage ride-through of the grid-connected doubly fed induction generator during severe grid faults. The rotor side converter and the grid side converter are controlled using an adaptive fuzzy logic controller topology under cascaded structure to improve the performance. The novel application of the ‘generalized variable step-size diffusion continuous mixed p-norm’ adaptive filtering algorithm is proposed to modify the calibrating factors of the fuzzy logic controllers at a rapid convergence speed with low normalized misalignment error. The proposed adaptive algorithm-based fuzzy logic controller has a better low voltage ride-through improvement capability than that of using the particle swarm optimization-based proportional-integral controller during severe grid disturbances. The convergence speed of the proposed adaptive filtering algorithm is compared to that of existing algorithms such as least mean fourth, least mean square, and continue mixed p-norm algorithms. In addition, a comparison is also made with different common optimization methods. The field-programmable gate array-based real-time experimental results are presented to validate the proposed adaptive control topology.

Regularity and Paracompactness in Fuzzy Topological Spaces

In this paper we obtain two characterizations of regular fuzzy topological spaces using Luo's and Abd El-Monsef and others' paracompact fuzzy topological spaces.

Fermatean Fuzzy CODAS Approach with Topology and Its Application to Sustainable Supplier Selection

A Fermatean fuzzy set (FFS) is a reliable method for representing uncertainty in “multi-criteria decision-making” (MCDM). This research seeks to examine the topological properties of FFSs and to establish the notion of “Fermatean fuzzy topology” (FFT). An FFT is the generalisation of existing fuzzy topologies. Several aspects of FFT are examined and various novel concepts are proposed, which include Fermatean fuzzy α-continuity between FFTSs and Fermatean fuzzy connectedness. To deal multiple challenges in sustainable supply chain management, a Fermatean fuzzy “combinative distance-based assessment” (CODAS) method was developed. The proposed FF CODAS technique involves various key features for MCDM. Firstly, a known reputation vector or equal expert weights is determined based on the reputation, experience and qualifications of the experts. Secondly, the Fermatean fuzzy direct rating approach is used to establish the relative relevance of criteria based on the expert group’s evaluation preferences. Thirdly, the Fermatean fuzzy CODAS approach is used to construct alternative orderings based on their assessment scores. Finally, an application is developed to show the benefit of the suggested supplier selection approach. Additionally, the symmetry of an optimal decision in application is carried out by a comparison analysis of the suggested models with some existing models.

A Relation between π Generalized Pre Connectedness and π Generalized Supra Connectedness In Intuitionistic Fuzzy Topological Space

The aim of this paper is to give the concepts of intuitionistic fuzzy generalized pre connectedness with study its properties. Finally we study the relation between intuitionistic fuzzy generalized pre connectedness and intuitionistic fuzzy generalized supra connectedness in intuitionistic fuzzy topological space .

On Fuzzy Star Refinement of Open Covering and imensions of Fuzzy Topological Spaces

In this paper the concepts of star-refinement and strongly star-refinement of covering are extended to fuzzy topological space in the sense of Chang, basic theorem for covering dimension of normal fuzzy topological space is proved. Also, the small inductive dimension function is extended to fuzzy topological space, and some results for this inductive dimension in Chang’s space are obtained.

On Fuzzy Star Refinement of Open Covering and imensions of Fuzzy Topological Spaces

In this paper the concepts of star-refinement and strongly star-refinement of covering are extended to fuzzy topological space in the sense of Chang, basic theorem for covering dimension of normal fuzzy topological space is proved. Also, the small inductive dimension function is extended to fuzzy topological space, and some results for this inductive dimension in Chang’s space are obtained.

On Semi- regular T1 and Semi- regular T2 in Intuitionistic Fuzzy Topological Spaces

The purpose of this paper is to give the new definitions of semi-regular T1 and semi-regular T2 separation axioms in intuitionistic fuzzy topological spaces. Study the basic properties, characterizations and relationships of these new concepts in intuitionistic fuzzy topological spaces.

A Relations between π Generalized α Connectedness and π Generalized Semi Connectedness in Intuitionistic Fuzzy Topological Spaces

The purpose of this paper is to introduce the concepts of intuitionistic fuzzy generalized α connectedness in intuitionistic fuzzy topological space and study some of its properties. Finally we study the relation between intuitionistic fuzzy generalized α connectedness and intuitionistic fuzzy generalized semi connectedness in intuitionistic fuzzy topological space

Topological approaches for n,m-Rung orthopair fuzzy sets with applications to diagnosis of learning disability

An n,m-rung orthopair fuzzy set is the one of the most useful expansions of fuzzy sets for coping with information uncertainties. In such circumstances, in this article, we define an n,m-rung orthopair fuzzy topology and investigate the basic aspects of this topology. We introduce their relationship with Fermatean fuzzy topology, Pythagorean fuzzy topology and intuitionistic fuzzy topology, and provide some examples. In addition, we introduce separated n,m-rung orthopair fuzzy sets and then we present the concept of diconnected n,m-rung orthopair fuzzy sets. Moreover, we study and characterize n,m-rung orthopair fuzzy continuous maps in great depth. Furthermore, we establish T0 and T1 in n,m-rung orthopair fuzzy topology and discover the links between them. Finally, we create a new relation extension on n,m-rung orthopair fuzzy sets and provide a method for classifying children with learning disabilities.

Topological structures on cubic bipolar fuzzy sets with linear assignment model and SIR method for healthcare

The idea of a cubic bipolar fuzzy set (CBFS) is a new hybrid extension of the cubic set (CS) and the bipolar fuzzy set (BFS). A CBFS is a strong model to deal with bipolarity and fuzziness in terms of positive membership grades (PMGs) and negative membership grades (NMGs). A positive interval and a positive numbers represent a PMG to express the degree of belongingness of a specific property, and a negative interval and a negative number represent a NMG which defines the degree of non-belongingness of the specific property (or satisfaction level of its counter property). The aim of this paper is to define the cubic bipolar fuzzy topology under P-order (CBFSP topology) as well as the cubic bipolar fuzzy topology under R-order (CBFSR topology). We investigate certain properties and results of CBFSP topology and CBFSR topology. Topological structures on CBFSs are helping in the development of new artificial intelligence (AI) techniques for healthcare domain strategies and investigating various critical diseases. Such techniques allow for the early detection and investigation of diseases, assisting clinicians in minimizing the possible risk factors. An extended linear assignment model (LAM) and superiority and inferiority ranking method (SIR method) are proposed for healthcare diagnosis based on newly developed structures. The proposed LAM and SIR method are successfully applied for investigation of critical diseases. Moreover, we discuss a comparison analysis of investigations made by suggested techniques with some existing approaches.

Q‐Rung Orthopair Picture Fuzzy Topological Spaces and Parameter‐Dependent Continuity: Control System Applications

This paper presents novel concepts in fuzzy topologies, namely q‐rung orthopair picture fuzzy (q‐ROPF) topology and q‐rung orthopair picture fuzzy point (q‐ROPFP). These concepts extended the existing notions in fuzzy topologies. We introduced a more relaxed form of continuity, called qε‐ROPF continuity, which allows for a flexible analysis of functions between q‐ROPF topological spaces by incorporating an error bound ε. We define the q‐neighborhood system for a q‐ROPF point in a q‐ROPF topological space and investigate the convergence of sequences of such points. Our results shed light on the behavior of functions and sequences in these spaces, as well as the conditions for uniqueness of limits within the realm of supports. This research has practical implications in control systems, providing valuable insights into the stability and robustness of the control strategies in the presence of small changes represented by the epsilon value.

NEW CHARACTERIZATIONS OF FUZZY TOPOLOGY

Following the generalization of Moore-Smith convergence of nets to fuzzy topological spaces which was given in Pu Pao-Ming, Liu Ying-Ming, \emph{Fuzzy topology I. Neighborhood structure of a fuzzy point and Moore-Smith convergence}, J. Math. Anal. Appl., \textbf{76} (1980), 571--599, a characterization theorem between fuzzy topologies and fuzzy convergence classes was introduced in Ying-Ming Liu, \emph{On fuzzy convergence classes}, Fuzzy Sets and Systems, \textbf{30} (1989), 47--51. Our goal in this paper is to provide modified versions of this characterization. Specifically, we will introduce the concept of fuzzy semi-convergence class to give an alternative characterization of fuzzy topology, in relation to the ordinary convergence of fuzzy nets, and then we will introduce the concept of fuzzy ideal convergence class to obtain analogous results, in relation to the ideal convergence of fuzzy nets.

An Introduction to M-Open Sets in Fuzzy Neutrosophic Topological Spaces

A new classes of sets called fuzzy neutrosophic M-open sets and fuzzy neutrosophic M-Closed sets in fuzzy neutrosophic topology are introduced some characterizations of these notions have been presented. After given the fundamental definitions of the new notions, we studided some theorems, propositions and some necessary relations with examples related to these notions had been discussed.