Fuzzy Continuity Research Articles

Fuzzy semi-I-open sets and fuzzy semi-I-continuity via fuzzy idealization

A new class of generalized fuzzy open called fuzzy semi-I-open sets is introduced via fuzzy idealization. Also their properties are obtained and given a decomposition of fuzzy continuity.

ON FUZZY FUNCTIONS

In 1998, Thakur and Singh introduce the concept of fuzzy fl-continuity (Fuzzy Sets and Systems, 98(1998), 383{391). In this paper we introduce and study the notion of fuzzy slightly fl- continuity. Fuzzy slightly fl-continuity generalize fuzzy fl-continuity. Moreover, basic properties and preservation therems of fuzzy slightly fl-continuous functions are obtained. 1. Introduction and preliminaries Fuzzy continuity is one of the main topics in fuzzy topology. Various authors introduce various types of fuzzy continuity. One of them is fuzzy fl-continuity. In 1998, Thakur and Singh introduce the concept of fuzzy fl-continuity.

Fuzzy UmUm-sets and fuzzy (U,m)(U,m)-continuous functions

Abstract In this paper the notions of fuzzy U m -sets and fuzzy ( U , m ) -open sets in fuzzy minimal spaces have introduced and some related basic results in this new setting are given. Further, some types of fuzzy continuity for fuzzy functions are investigated.

INTUITIONISTIC FUZZY RETRACTS

The concept of a intuitionistic fuzzy topology (IFT) was introduced by Coker 1997. The concept of a fuzzy retract was introduced by Rodabaugh in 1981. The aim of this paper is to introduce a new concepts of fuzzy continuity and fuzzy retracts in an intuitionistic fuzzy topological spaces and establish some of their properties. Also, the relations between these new concepts are discussed.

Fuzzy bounded linear operators

In this paper, a notion of boundedness of a linear operator from a fuzzy normed linear space to another fuzzy normed linear space is introduced and two types (strong and weak) of fuzzy bounded linear operators are defined. Relation between fuzzy continuity and fuzzy boundedness is studied. Definitions of fuzzy bounded linear functionals are given and the notions of fuzzy dual spaces are developed. The Hahn-Banach theorem, the Open mapping theorem, the Closed graph theorem and the Uniform boundedness principle theorem are established.

INTUITIONISTIC FUZZY FUNCTIONS

In this paper, we generally introduce some of the terminology of Yalvac [10] and Azad [4] in intuitionistic fuzzy topological spaces. In addition to the fundamental concepts of intuitionistic fuzzy sets, we emphasize the usefulness of the concepts of intuitionistic fuzzy points intuitionistic fuzzy elementhood. Mainly, this paper is devoted to the study of intuitionistic fuzzy topological spaces with specific attention to the weaker forms of fuzzy continuity.

γ-Connectedness in fuzzy topological spaces

The aim of this paper is to introduce the concept <TEX>$\gamma$</TEX>-connectedness in fuzzy topological spaces. We also investigate some interre lations between this types of fuzzy connectedness together with the preservation properties under some types of fuzzy continuity. A comparison between some types of connectedness in fuzzy topological spaces is of interest.

A note on the article “Fuzzy totally continuous and totally semi-continuous functions”

A. Mukherjee has introduced the concepts of fuzzy totally continuous and fuzzy totally semi-continuous functions in 1999. Apart from the fact that fuzzy total continuity and fuzzy total semi-continuity were introduced in Mukherjee's paper without regard for whether they are topological notions (i.e. give rise to topological categories) or for whether there are deep, canonical examples of such concepts, we show in this note that there are mathematical errors in some of the claimed results of the paper as well.

Fuzzy cγ‐open sets and fuzzy cγ‐continuity in fuzzifying topology

The concepts of fuzzy cγ‐open sets and fuzzy cγ‐continuity are introduced and studied in fuzzifying topology and by making use of these concepts, some decompositions of fuzzy continuity are introduced.

On first countable [formula omitted]-fuzzy topological spaces

The fuzzy continuity of a bijective function defined on a first countable, C 1 , L-fuzzy topological space where L is a spatial frame is characterized by using the sequences of L-fuzzy points. Moreover, a local characterization of fuzzy continuity is given.

Pre-Continuity and [formula omitted]-continuity in fuzzifying topology

The concepts of fuzzy pre-continuity and fuzzy cpre-continuity are introduced and studied in fuzzifying topology essentially in order to give decompositions of fuzzy continuity.

Starplus-Compactness and Starplus-Compact Open Fuzzy Topologies on Function Spaces

Extending Lowen's notion of strong fuzzy compactness to an arbitrary fuzzy set the notion of a starplus-compact fuzzy set is introduced. It is shown that the category of starplus-compact fuzzy topological spaces is productive, and that starplus-compactness is a good extension of the notion of compactness. It is shown that the class of starplus-compact fuzzy sets is pseudo closed hereditary and invariant under fuzzy continuous maps. Moreover, the notion of starplus-compact open fuzzy topology on a function space is introduced and its interrelations with the fuzzy topology of pointwise convergence and the fuzzy topology of joint fuzzy continuity are studied. It is shown that a fuzzy topology on a function space which is jointly fuzzy continuous on starplus-compacta is finer than the starplus-compact open fuzzy topology. Sufficient conditions on function spaces are obtained for the starplus-compact open fuzzy topology and the fuzzy topology of joint fuzzy continuity on starplus-compacta to coincide.

Formula omitted]-continuity and [formula omitted]-continuity in fuzzifying topology

The concepts of α-continuity and cα-continuity are considered and studied in fuzzifying topology and by making use of these concepts, some decompositions of fuzzy continuity are introduced. It is proved that the family of all α-sets in fuzzifying topology may not be a fuzzifying topology.

A Tychonoff theorem in intuitionistic fuzzy topological spaces

The purpose of this paper is to prove a Tychonoff theorem in the so‐called “intuitionistic fuzzy topological spaces.” After giving the fundamental definitions, such as the definitions of intuitionistic fuzzy set, intuitionistic fuzzy topology, intuitionistic fuzzy topological space, fuzzy continuity, fuzzy compactness, and fuzzy dicompactness, we obtain several preservation properties and some characterizations concerning fuzzy compactness. Lastly we give a Tychonoff‐like theorem.

An introduction to intuitionistic fuzzy topological spaces

The purpose of this paper is to construct the basic concepts of the so-called “intuitionistic fuzzy topological spaces”. After giving the fundamental definitions and the necessary examples we introduce the definitions of fuzzy continuity, fuzzy compactness, fuzzy connectedness and fuzzy Hausdorff space, and obtain several preservation properties and some characterizations concerning fuzzy compactness and fuzzy connectedness.

Neoclassical analysis: Fuzzy continuity and convergence

The neoclassical analysis is a field in which fuzzy continuous functions are investigated. For this purpose, new measures of continuity and discontinuity (or defects of continuity) are introduced and studied. Based on such measures, classes of fuzzy continuous functions are defined and their properties are obtained. The class of fuzzy continuous functions may be considered as a fuzzy set of continuous functions. Its support consists of all functions on some topological space X into a metric space Y and its membership function is the corresponding continuity measure. Such an expansion provides a possibility to complete some important classical results. Connections between boundedness and fuzzy continuity are investigated. Criteria of boundedness and local boundedness are obtained for functions on Eucleadean spaces. Besides, such new concepts as fuzzy convergence and fuzzy uniform convergence are introduced and investigated. Their properties and connections with fuzzy continuous functions are explicated. Some results, which are obtained here, are similar to the results of classical mathematical analysis, while others differ essentially from those that are proved in classical mathematics. In the first case classical results are consequences of the corresponding results of neoclassical analysis.

Fuzzy s-continuous functions and semilocally connected fuzzy topological spaces

The concept of s-continuous functions (Kohli, 1978) is translated in fuzzy setting into two concepts, fuzzy s-continuous functions and fuzzy os-continuous functions. The concepts of semiconnected functions (Kohli, 1978) and semilocally connected spaces (Kohli, 1978) do the same. Interactions between those concepts in fuzzy setting and fuzzy continuity (Chang, 1968) are discussed. Also, characterizations of semilocally connected and semilocally o-connected fuzzy topological spaces in terms of fuzzy s-continuous functions and fuzzy os-continuous functions, respectively, are obtained.

Semi-open sets, semi-continuity and semi-open mappings in fuzzy bitopological spaces

Abstract In this paper, the concepts of fuzzy semi-open sets, fuzzy semi-continuity and fuzzy semi-open mappings due to Azad [J. Math. Anal. Appl. 82 (1981) 14–32] have been generalized to the fuzzy bitopological setting and some of its basic properties are discussed. Several characterizing theorems of fuzzy semi-continuity and its relationship with fuzzy continuity are investigated.

Fuzzy separation axioms and fuzzy continuity in fuzzy bitopological spaces

Let ( X, τ 1, τ 2) be a bitopological space and ω( τ i ) ( i = 1, 2) be the set of all lower semi-continuous functions defined from X into the closed unit interval [0, 1]. In this paper we have succeeded in showing goodness of extension of separation axioms for fuzzy bitopological spaces, namely we prove the space ( X, τ 1, τ 2) is P-T i , P-T iw , P-regular, and P-normal iff the fuzzy bitopological space ( X, ω( τ 1), ω( τ 2)) is P-T i , P-T iw , P-regular and P-normal.

Fuzzy faintly continuous functions

The aim of this paper is to introduce the concepts of fuzzy faintly continuous functions. These functions have been characterized and investigated mainly in the light of the notions of quasi-concidence, q-neighbourhoods, fuzzy θ-interior and fuzzy θ-closure. It is seen that fuzzy continuity implies fuzzy faintly continuity, but not conversely. The converse is also true if the co-domain of the function is a fuzzy regular space. Finally a comparative study regarding the mutual interrelations among the fuzzy R -map, fuzzy completely continuous, fuzzy almost continuous and fuzzy continuous functions along with fuzzy faintly continuous functions is made.