Fuzzy Continuity Research Articles

Fuzzy continuity via fuzzy C-open sets

In fuzzy topological space, the concepts of fuzzy continuity are developed by applying fuzzy open sets. In this paper the notions of fuzzy continuity are investigated using fuzzy C -open sets, where C is an arbitrary complement function C: [0,1] → [0,1] and some of their properties are studied.

Fuzzy continuity via fuzzy C-open sets

In fuzzy topological space, the concepts of fuzzy continuity are developed by applying fuzzy open sets. In this paper the notions of fuzzy continuity are investigated using fuzzy C -open sets, where C is an arbitrary complement function C: [0,1] → [0,1] and some of their properties are studied.

Intuitionistic Fuzzy Topological Spaces Model

The fusion of technology and science is a very complex and scientific phenomenon that still carries mysteries that need to be understood. To unravel these phenomena, mathematical models are beneficial to treat different systems with unpredictable system elements. Here, the generalized intuitionistic fuzzy ideal is studied with topological space. These concepts are useful to analyze new generalized intuitionistic models. The basic structure is studied here with various relations between the generalized intuitionistic fuzzy ideals and the generalized intuitionistic fuzzy topologies. This study includes intuitionistic fuzzy topological spaces (IFS); the fundamental definitions of intuitionistic fuzzy Hausdorff space; intuitionistic fuzzy regular space; intuitionistic fuzzy normal space; intuitionistic fuzzy continuity; operations on IFS, the compactness and separation axioms.

Pythagorean fuzzy topological spaces

In the present paper, we introduce the notion of Pythagorean fuzzy topological space by motivating from the notion of fuzzy topological space. We define Pythagorean fuzzy continuity of a function defined between Pythagorean fuzzy topological spaces and we characterize this concept. Using the concept of continuity, we also give a method to construct a Pythagorean fuzzy topology on a given non-empty set.

On Lembda Gamma- Set in Fuzzy Bitopological Spaces

The aim of this paper is to introduce the concept of lambda operator of a fuzzy set in a fuzzy bitopological space. Then we study (i, j)-fuzzy Lembda Gamma- set and its properties. Moreover we define (i, j)-fuzzy Lembda-closed set, (i, j)-fuzzy Lembda Gamma-closed set and (i, j)-fuzzy generalized closed set in fuzzy bitopological space. The concepts (i, j)-fuzzy Lembda-closed set and (i, j)-fuzzy generalized closed set are independent to each other but jointly they gives the taui-fuzzy closed set. To this end as the application of (i, j)-fuzzy Lembda Gamma-closed set we shall study (i, j)-fuzzy Lembda Gamma continuity and (i, j)-fuzzy Lembda Gamma-generalized continuity and their properties.

Ps-ro fuzzy strongly α-irresolute function

Abstract The prime objective of this paper is to introduce and characterize a new type of function in a fuzzy topological spaces called ps-ro fuzzy strongly α-irresolute function. The interrelations of this function with the parallel existing allied concepts are established. The independence of ps-ro fuzzy strongly α-irresolute and well known concept of fuzzy strongly α-irresolute function motivate authors to explore it. Also, this function is found to be stronger than ps-ro fuzzy continuity, ps-ro fuzzy semicontinuity, ps-ro fuzzy precontinuity and ps-ro fuzzy α-continuity. Further, several characterizations of these functions along with different conditions for their existence are obtained.

English

In this study, some definitions and features related to fuzzy continuity, fuzzy membership functions and fuzzy continuous functions are examined. Using these definitions and properties, some theorems about fuzzy continuous functions have been proved. Key words: Fuzzy continuity, fuzzy function, fuzzy set.

On Fuzzy e^*-Open Sets and Fuzzy (D,S)^*-Sets

The aim of this paper is to introduce some new classes of fuzzy sets and some new classes of fuzzy continuity namely fuzzy e ∗ -open sets, fuzzy (D, S)-sets, fuzzy (DS, ε)-sets, fuzzy (D, S)∗ -sets, fuzzy (DS, ε) ∗ -sets, fuzzy e-continuity, fuzzy (D, S)∗ - continuity and fuzzy (DS, ∈)∗ -continuity. Properties of these new concepts are investigated. Moreover, some new decompositions of fuzzy continuity are provided.

The functional space in fuzzy analysis

In this paper, we briefly summarize some work on the area of functional spaces in fuzzy analysis and devoted to four directions. The first direction is the development of the fuzzy functional analysis on the setting of topological linear space and several kinds of fuzzy normed linear spaces. Next direction is fuzzy number spaces with different metrics and the embeddings to concrete functional spaces with a linear structure. The third direction is fuzzy continuous function spaces and the approximation by multilayer regular fuzzy neural networks for various fuzzy continuities. The last direction is the space of measurable functions and the space of (Sugeno)-integrable functions based on the theory of monotonic measures. In this paper, we also present several suggestions on future research. Wu Congxin was an undergraduate student of the Mathematics Department of Northeastern Peoples University during 1952-1955, and Professor Hsu guided and supported him so much for long time.

On $\delta$-continuity in mixed fuzzy topological spaces

In this paper we introduce and study the notion of d-continuity continuity on mixed fuzzy topological spaces. We have investigated this notion in the light of the notion of q-neighbourhoods, q-coincidence, fuzzy d-closure, fuzzy d-interior. In this paper we have established the relationship between fuzzy continuity and fuzzy d-continuity in mixed fuzzy topological spaces.

Non-archimedean Intuitionistic Fuzzy Continuity Of Dectic Mappings

In this paper, we investigate the non-Archimedean intuitionistic fuzzy continuity through the existence of a certain solution of a fuzzy stability problem for the system of additive-quadratic-cubic-quartic functional equations.

<b>Weakly continuous functions on mixed fuzzy topological spaces<b>

The notions of continuity was generalized in the fuzzy setting by Chang (1968). Later on Azad (1981) introduced some weaker form of fuzzy continuity like fuzzy almost continuity, fuzzy semi-continuity and fuzzy weak continuity. These are natural generalization of the corresponding weaker forms of continuity in topological spaces. Recently Arya and Singal (2001a and b) introduce another weaker form of fuzzy continuity, namely fuzzy subweakly continuity as a natural generalization of subweak continuity introduced by Rose (1984). In this paper we introduce fuzzy weak continuity in mixed fuzzy topological space.

Fuzzy Perfect Mappings and [formula omitted]-Compactness in Smooth Fuzzy Topological Spaces

We point out that the product of two fuzzy closed sets of smooth fuzzy topological spaces need not be fuzzy closed with respect to the the existing notion of product smooth fuzzy topology. To get this property, we introduce a new suitable product smooth fuzzy topology. We investigate whether F1×F2 and (F,H) are weakly smooth fuzzy continuity whenever F1, F2, F and H are weakly smooth fuzzy continuous. Using this new product smooth fuzzy topology, we define smooth fuzzy perfect mapping and prove that composition of two smooth fuzzy perfect mappings is smooth fuzzy perfect under some additional conditions. We also introduce two new notions of compactness called Q-compactness and Q-α-compactness; and discuss the compactness of the image of a Q-compact set (Q-α-compact set) under a weakly smooth fuzzy continuous function ((α,β)-weakly smooth fuzzy continuous function).

English

In this paper, I have studied some properties of fuzzy soft topological space. We define fuzzy soft intuitionistic separation axioms and basic definition of intuitionistic fuzzy soft normal spaces and theorems. Lastly, introduced intuitionistic fuzzy soft completely normal spaces. There are many problems encountered in real life. Various mathematical set theories such as soft set initiated by Molodtsov(2) in 1999 for modeling uncertainty present in real life. Xio(13) and Pie and Mio (3) discussed the relationship between soft sets is a parameterized classification of the objects of the universe. Atanassov (7) introduced the fundamental concept of intuitionistic fuzzy topological spaces, fuzzy continuity , fuzzy compactness and some other related concepts. Mahanta and Das(6) established the neighbourhood structures in fuzzifying topological spaces. Some others (1),(4),(8),(10).studied some separation axioms and their separation axioms are discussed on crisp points not on fuzzy points. My main aim in this paper is to develop the basic properties of intuitionistic fuzzy soft separation axioms and established several equivalent forms of fuzzy soft spaces.

On $ps$-$ro$ semiopen fuzzy set and $ps$-$ro$ fuzzy semicontinuous, semiopen functions

The aim of this paper is to introduce and characterize ps-ro semiopen (semiclosed) fuzzy sets, which are totally independent of the existing notion of fuzzy open (closed) sets and semiopen (semiclosed) fuzzy sets. Also, in term of these fuzzy sets and operators ps-scl and ps-sint, a class of functions named as ps-ro fuzzy semicontinuous and ps-ro fuzzy semiopen (closed) functions are dened and their various properties are studied. ps-ro fuzzy semicontinuity is indeed totally dierent from both the existing concepts of fuzzy continuity and fuzzy semicontinuity. Similarly, ps-ro fuzzy open (closed) and well known concept of fuzzy semiopen (closed) functions do not imply each other. These concepts are used as new tools to study dierent characterizations of the given fuzzy topological space, giving a new dimension in the study of fuzzy topological spaces.

Fuzzy Quasi C*-algebra

At the present paper, the new concepts of fuzzy quasi norm, fuzzy Banach space, fuzzy quasi continuity and fuzzy quasi boundedness is introduced. Furthermore, we define the fuzzy quasi operator norm and also it is shown that the set all of fuzzy quasi bounded operator from X to Y is fuzzy quasi Banach space. Finally, we have introduced and investigated some notions and some results on *-algebra theory.

Stability Results in Intuitionistic Fuzzy Normed Spaces for a Cubic Functional Equation

In this paper, we determine some stability results concerning the cubic functional equation kf(x + ky) + f(kx y) = k(k 2 + 1) 2 (f(x + y) + f(x y)) + (k 4 1)f(y), where k � 2 is a fixed integer, in the setting of intuitionistic fuzzy normed spaces (IFNS). Further we study the intuitionistic fuzzy continuity through the existence of a certain solution of a fuzzy stability proble m for approximately cubic functional equation.

Generalised Fuzzy Continuous Maps in Fuzzy Topological Spaces

The study of continuity and its weaker forms constitutes an established branch of investigation in general topological spaces. Recently some researchers have tried to extend these studies to the broader framework of fuzzy topological spaces. N. Ajmal proposed a theory of localization in the study of continuity and its weaker forms in fuzzy setting. Using two notions of membership of a fuzzy point to a fuzzy set, neighborhood structure of fuzzy point and quasineighborhood structure of a fuzzy point, an investigation of fuzzy continuity, fuzzy alfa- continuity, fuzzy beta- continuity functions, and fuzzy almost quasi continuous functions have been carried out in the present study. The purpose of this paper is to introduce and study the concepts of generalized fuzzy continuous maps, which includes the class of fuzzy continuous maps. Keywords - Mathematics, Fuzzy Topology, Fuzzy Topological Spaces, Fuzzy Continuous Maps, Andhra Pradesh, India

Fuzzifying topologies on the space of linear operators

We introduce the notion of fuzzifying topologies on the space of linear operators. The concepts of fuzzifying topologies of pointwise convergence, bounded convergence, and complete bounded convergence are presented. We prove a sufficient and necessary condition for which the fuzzifying topologies are compatible with the structure on the space of linear operators. The Hausdorff separation of a fuzzifying topology on the space of linear operators is discussed. Specially, the net convergence, fuzzy boundedness, and fuzzy continuity of evaluation mappings in the fuzzifying topological linear space of pointwise convergence are investigated.

Fuzzy boundedness and contractiveness on intuitionistic 2-fuzzy 2-normed linear space

The concepts of fuzzy boundedness, fuzzy continuity and intuitionistic fuzzy 2- contractive mapping on intutionistic 2-fuzzy 2-normed linear space are introduced. Using these concepts some theorems are proved.