Fuzzy Continuous Functions Research Articles

Fuzzy SSPO-separation Axioms and Fuzzy α-SSPO Compactness

In this paper we will introduce the concept of new separation axioms named fuzzy SSPO-separation axioms by using the fuzzy strong semi preopen sets and we will also introduce and investigate properties of (alpha)-SSPO compactness. We will define and investigate relation between fuzzy separation axioms, fuzzy pre-separation axioms and different forms of fuzzy continuous mappings. We will also investigate the existence of a countable base of fuzzy strong semi preopen sets, we will define the concept of SSPO separability, the concept of (alpha)-SSPO Lindelof sets and examine their properties. With the concept of fuzzy strong semi pre-continuity, SSPO-irresolute continuous mappings and other forms of fuzzy continuity, we will investigate the new concept of fuzzy compactness and its properties in regards to the mentioned mappings.

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.

Four Types of Generalized Fuzzy Continuous Mappings

Four Types of Generalized Fuzzy Continuous Mappings

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.

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.

Fuzzy Continuous Mappings on Fuzzy F-Spaces

In the present paper, we first introduce different types of fuzzy continuity for mappings between fuzzy F-normed linear spaces and the relations between them are investigated. Secondly, the principles of fuzzy functional analysis are established in the context of fuzzy F-spaces. More precisely, based on the fact that fuzzy continuity and topological continuity are equivalent, we obtain the closed graph theorem and the open mapping theorem. Using Zabreiko’s lemma, we prove the uniform bounded principle and Banach–Steinhaus theorem. Finally, some future research directions are presented.

Local and Global Existence and Uniqueness of Solution for Class of Fuzzy Fractional Functional Evolution Equation

For fuzzy fractional functional evolution equations, the concept of global and local existence and uniqueness will be presented in this work. We employ the contraction principle and successive approximations for global and local existence and uniqueness, respectively, as given 0 c D q H x I = f I , x I + ∫ 0 I g I , s , x s ds , I ≥ I 0 , I ∈ 0 , T , x I = ψ I − I 0 = ψ 0 ∈ C σ , I 0 ≥ I ≥ I 0 − σ , x ′ I = ψ ′ I = ψ 1 , where C σ denotes the set of fuzzy continuous mapping defined on I 0 − σ , T and σ > 1 . We also use this method to solve fuzzy fractional functional evolution equations with fuzzy population models and distributed delays using fuzzy fractional functional evolution equations. To explain these results, some theorems are given. Finally, certain fuzzy fractional functional evolution equations are illustrated.

The Product Fuzzy Metric Space and its Basic Properties

A new type of FMS, known as a product FMS (or simply p-FMS) is introduced, the reason behind this name is the continuous t-norm used here is binary operation usually product between number in [0, 1]. To show that this type of spaces is exists we give some examples, then some important basic properties, of this space are introduced with its proves. Moreover we study fuzzy continuous and uniformly fuzzy continuous function by proving basic properties of these notions. Furthermore the prove of cross product of finite number of p-FMS is again a p-FMS is introduced.

SOME PROPERTIES OF T0 FUZZY SOFT TOPOLOGICAL SPACES IN QUASI-COINCIDENCE SENSE

In this paper, we have introduced and studied some new notions of T0 separation axiom in fuzzy soft topological spaces using quasi-coincident relation for fuzzy soft points. We have shown a relationship between ours and other counterparts and observed that all these notions satisfy good extension, hereditary, productive, and projective properties. Moreover, we have also shown that these notions are preserved under one-one, onto, and fuzzy soft continuous mappings. Finally, initial and final soft topologies are studied also.

Some properties of (r,s)-generalized fuzzy semi-closed sets and some applications

In this work, the notion of \((r,s)\)-generalized fuzzy semi-closed sets is introduced and some properties are given. Also, we show that every \((r,s)\)-generalized fuzzy closed set by Abbas (2006) is \((r,s)\)-generalized fuzzy semi-closed set, but the converse need not be true. After that, the generalized forms of fuzzy continuous mappings between double fuzzy topological spaces \((X,\tau_{1}, \tau_{1}^*)\) and \((Y,\tau_{2}, \tau_{2}^*)\) are introduced and studied. Some interesting relationship between these mappings and other mappings introduced previously are investigated with the help of examples. In the end, the notion of \((r,s)\)-fuzzy GS-connected sets is introduced and studied with help of \((r,s)\)-generalized fuzzy semi-closed sets.

Nano Fuzzy b-open Sets in Nano fuzzy Topological Spaces

The purpose of this paper is to define and study a new class of Nano fuzzy open sets called Nano fuzzy b-open sets in Nano fuzzy topological spaces. We have tried to analyze the basic properties of Nano fuzzy b-open sets. We have also used these Nano fuzzy b-open sets to introduce a new type of Nano fuzzy continuous functions, which are called Nano fuzzy b-open continuous functions and their properties are investigated.

Picture fuzzy topological spaces and associated continuous functions

<abstract> <p>This paper describes a study of picture fuzzy topological spaces. We prove some basic results related to picture fuzzy sets together with the introduction of new notions such as the rank, picture fuzzy base and picture fuzzy sub-base of picture fuzzy topological spaces. With the help of these notions, we present a method to design picture fuzzy topological spaces. Furthermore, we introduce the concept of continuity to picture fuzzy topological spaces and find a necessary and sufficient condition for a picture fuzzy continuous function between two picture fuzzy topological spaces.</p> </abstract>

Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function

The theories of metric spaces and fuzzy metric spaces are crucial topics in mathematics. 
 Compactness is one of the most important and fundamental properties that have been widely used in Functional Analysis. In this paper, the definition of compact fuzzy soft metric space is introduced and some of its important theorems are investigated. Also, sequentially compact fuzzy soft metric space and locally compact fuzzy soft metric space are defined and the relationships between them are studied. Moreover, the relationships between each of the previous two concepts and several other known concepts are investigated separately. Besides, the compact fuzzy soft continuous functions are studied and some essential theorems are proved.

Design and evaluation of a interval valued intuitionistic multi fuzzy completely generalized semipre continuous mappings

Fuzzy sets introduced to overthrow the uncertainty of an object. Interval valued intuitionistic fuzzy sets in topological structure space is an extension of fuzzy sets. Interval-valued intuitionistic multi fuzzy set theory is a capable tool for commerce with ambivalence of expertise in information systems. The motive of this paper is to present interval valued intuitionistic multi fuzzy completely generalized semiprecontinuous mappings and provide some of their properties. Also we proved the relation between various types of interval valued intuitionistic multi fuzzy continuous mappings. AMS Subject Classification (2010): 54A40.

The Continuity of Fuzzy Metric Spaces

<p>In the present paper, the definitions of a fuzzy continuous function and uniformly fuzzy continuous are introduced. we prove that a function from a fuzzy metric space ( ) into a fuzzy metric space ( ) is fuzzy continuous if and only if for every fuzzy open subset of , is fuzzy open in . Also the composition function of two uniformly fuzzy continuous functions is proved to be a uniformly fuzzy continuous function.</p>

Fuzzy pairwise regular bitopological spaces in quasi-coincidence sense

This paper introduces three notions of fuzzy pairwise regular between bitopological spaces in quasi-coincidence sense. Then, we investigate some relations between ours and other counterparts. We observe that all these concepts are preserved under one-one, onto, fuzzy closed, fuzzy open, and fuzzy continuous mappings. Also, the hereditary property is satisfied by these concepts.
 Journal of Bangladesh Academy of Sciences, Vol. 44, No. 2, 139-143, 2020

(3, 2)-Fuzzy Sets and Their Applications to Topology and Optimal Choices.

The purpose of this paper is to define the concept of (3, 2)-fuzzy sets and discuss their relationship with other kinds of fuzzy sets. We describe some of the basic set operations on (3, 2)-fuzzy sets. (3, 2)-Fuzzy sets can deal with more uncertain situations than Pythagorean and intuitionistic fuzzy sets because of their larger range of describing the membership grades. Furthermore, we familiarize the notion of (3, 2)-fuzzy topological space and discuss the master properties of (3, 2)-fuzzy continuous maps. Then, we introduce the concept of (3, 2)-fuzzy points and study some types of separation axioms in (3, 2)-fuzzy topological space. Moreover, we establish the idea of relation in (3, 2)-fuzzy set and present some properties. Ultimately, on the basis of academic performance, the decision-making approach of student placement is presented via the proposed (3, 2)-fuzzy relation to ascertain the suitability of colleges to applicants.

Topological Structure of Fuzzy PU-new Ideal in PU-algebra

In this manuscript, we consider the fuzzification of the notion PU-new ideal of PU-algebra and define the fuzzy topological terms such that fuzzy topology, <i>τ</i>-open fuzzy set, fuzzy neighborhood, fuzzy interior, sequence of fuzzy sets, fuzzy neighborhood system, fuzzy continuity of a function with respect to PU-new ideal of PU-algebra. We explore the new theorems and related properties of above mention notions with respect to PU-new ideal on PU-algebras. Such that for (Ⱬ,<i> τ</i>) to be a TSFP on Ⱬ and the set Ḟ is a fuzzy in Ⱬ and N<SUB>Ḟ</SUB> be a fuzzy neighborhood system of Ḟ then the finite intersection of elements of ‘N<SUB>Ḟ</SUB>’ is also an element of ‘N<SUB>Ḟ</SUB>’ also any fuzzy set of Ⱬ which contains an element of “N<SUB>Ḟ</SUB>” is also an element of “N<SUB>Ḟ</SUB>”. Furthermore we prove the conditions with respect to fuzzy neighborhood, convergence of a sequence of fuzzy sets, fuzzy interior set of a fuzzy set under which a fuzzy set <I>Ḟ</I> is <i>τ</i>-open. We show that how the function Ψ from (Ⱬ₁,<i>τ</i>) to (Ⱬ₂,ω) is fuzzy continuous. We prove that if Ψ is a fuzzy continuous function then for every fuzzy set <I>Ḟ</I> in Ⱬ₁, inverse of each neighborhood of Ψ(<I>Ḟ</I>) is a neighborhood of a fuzzy set <I>Ḟ</I>.

Generalized Fuzzy Continuous Maps and Generalized Fuzzy Closed Maps in Fuzzy Biclosure Space

The aim of this paper is to introduce the notion of generalized fuzzy continuous maps and generalized fuzzy closed maps in fuzzy biclosure spaces by using the concept of generalized fuzzy closed set briefly a g -fuzzy closed set. In this paper study and investigation of some important properties and characterizations of generalized fuzzy continuous maps and generalized fuzzy closed maps in fuzzy biclosure spaces has also been done.

Construction of Intuitionistic Fuzzy Mappings with Applications

In a recent paper, Ismail and Massa'deh have introduced the notion of L-fuzzy mapping and some basic operations were proved. In this paper, we generalize this notion to the setting of intuitionistic fuzzy sets. Moreover, we study the main properties related to intuitionistic fuzzy mapping. As applications, we provide properties of intuitionistic fuzzy continuous mappings in intuitionistic fuzzy topological spaces and investigate the relation among various kinds of intuitionistic fuzzy continuity.