Fuzzy Compact Research Articles

The Properties of the Spectrals of Fuzzy Compact Linear Operators

The objective of this paper is to present a novel approach for the a-fuzzy standardized area and its fundamental characteristics with basic attributes of fuzzy compact and fuzzy bounded linear functions. Also, it presents some of the basic attributes of the spectral of fuzzy compact linear functions in terms of theorems that clearly draw the elementary properties of these functions and the mathematical relationships between them.

Fuzzy Convergence Sequence and Fuzzy Compact Operators on Standard Fuzzy Normed Spaces

The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit where linear operator from complete standard fuzzy normed space into a standard fuzzy normed space then belongs to the set of all fuzzy bounded linear operators . Furthermore, the concept of a fuzzy compact linear operator in a standard fuzzy normed space is introduced. Also, several fundamental theorems of fuzzy compact linear operators are studied in the same space. More accurately, every fuzzy compact linear operator is proved to be fuzzy bounded where and are two standard fuzzy normed spaces

Some Properties of Fuzzy Compact Algebra Fuzzy Normed Spaces and Finite Dimensional Algebra Fuzzy Normed Spaces

Our goal in this article is to recall the notion of algebra fuzzy normed space and its basic properties to introduce the notion of fuzzy compact algebra fuzzy normed space. Then some properties of fuzzy compact algebra fuzzy normed spaces are proved. After that, we study a finite dimensional algebra fuzzy normed space and we proved some properties that algebra fuzzy normed spaces do not admit it.

Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and its Fuzzy Compactness

In this paper, we first investigate the relationship between various notions of fuzzy boundedness of linear operators in fuzzy normed linear spaces. We also discuss the fuzzy boundedness of fuzzy compact operators. Furthermore, the spaces of fuzzy compact operators have been studied.

Properties of Fuzzy Compact Linear Operators on Fuzzy Normed Spaces

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact operators. Finally, if T belongs to FC(V,U) and dimension of V is finite then T is fuzzy compact is proved.

Separation Axioms in Intuitionistic Fuzzy Compact Topological Spaces

Separation Axioms in Intuitionistic Fuzzy Compact Topological Spaces

The Relations between Characterized Fuzzy Proximity, Fuzzy Compact, Fuzzy Uniform Spaces and Characterized Fuzzy Ts–Spaces and Fuzzy Rk–Spaces

In this research work, we study the relations between the characterized fuzzy Ts–spaces and characterized fuzzy Rk–spaces presented in old papers, for s ∈ {0,1,2,3,3 1/2 ,4} and k ∈ {1,2,2 1/2 ,3} and the characterized fuzzy proximity spaces presented. We also study the relations between the characterized fuzzy Ts–spaces, the characterized fuzzy Rk–spaces and the characterized fuzzy compact spaces which is presented in old paper, as a generalization of the weaker and stronger forms of the G–compactness defined by Gahler. Moreover, we show here the relations between these characterized fuzzy Ts–spaces, characterized fuzzy Rk–spaces and the characterized fuzzy uniform spaces introduced and studied by Abd-Allah in 2013 as a generalization of the weaker and stronger forms of the fuzzy uniform spaces introduced by Gahler.

Local fuzzy compactness with respect to fuzzy ideal

Given a nonempty set X, a fuzzy ideal I on X is a collection of subsets of X closed under finite union and subset operations. In this paper we define a space to be locally I fuzzy compact space if every point in the space has an I fuzzy compact neighbourhood. Basic results concerning locally I fuzzy compact spaces are given relating to subspaces, preservation of functions, and products. Classical results concerning locally fuzzy compact spaces are obtained by I ={φ},and certain results for locally H-closed spaces are obtained by letting I be the fuzzy ideal of nowhere dense sets. Locally H-closed spaces are characterized in the category of Hausdorff spaces as being the locally nowhere-dense-fuzzy compact sets.

A new definition of fuzzy compactness

In this paper, a new definition of fuzzy compactness is presented in L-topological spaces when L is a complete DeMorgan algebra. This definition does not rely on the structure of the basis lattice L and no distributivity in L is required. The intersection of a fuzzy compact L-set and a closed L-set is fuzzy compact. The continuous image of a fuzzy compact L-set is fuzzy compact. If the set of all prime elements of L is order generating, then the Alexander Subbase Theorem is true. When L is a completely distributive DeMorgan algebra, it is equivalent to Lowen's fuzzy compactness, and in this case, its many characterizations are presented by means of open L-sets and closed L-sets.

Strong fuzzy compact sets and ultra-fuzzy compact sets in L-topological spaces

In this paper, Lowen's strong fuzzy compactness and ultra-fuzzy compactness of I-topological spaces are extended to L-subsets, for L—a complete lattice. The properties of strong fuzzy compact L-subsets and ultra-fuzzy compact L-subsets are studied in detail here, and comparisons between these notions as well as the notion of N-compactness are shown.

Paracompactness in L-topological spaces

In this paper a certain fuzzy paracompactness is presented by means of the concept of α-locally finite family of L-fuzzy sets. The concept of α-locally finite family can be used to characterize fuzzy countable compactness. This fuzzy paracompactness is a natural generalization of Lowen fuzzy compactness. A fuzzy countably compact L-set is fuzzy paracompact if and only if it is fuzzy compact. A topological space (X, T) is paracompact if and only if its induced space (X,ω( T)) is fuzzy paracompact. When ms( L)⩽ ω, the fuzzy enhanced real line R ̃ (L) is fuzzy paracompact. The product of a fuzzy compact set and a fuzzy paracompact set is fuzzy paracompact. A fuzzy strongly T 2 paracompact space is strongly S ∗ -regular and strongly WS ∗ -normal. Moreover a strongly S ∗ -regular Lindelöf space is fuzzy paracompact.

On compactness of induced I( L)-fuzzy topological spaces

The induced I( L)-fuzzy topological spaces for L-fuzzy topological spaces introduced by Wang Geping is a kind of important fuzzy topological space. In this paper, the author studies the fuzzy compactness of induced I( L)-fuzzy topological spaces. Some available relations between molecular nets of an L-fuzzy topological space and that of its induced I( L)-fuzzy topological space are firstly presented. By using these relations, the author obtains that the induced I( L)-fuzzy topological space is strong fuzzy compact (resp. fuzzy compact, N-compact) if and only if the L-fuzzy topological space is strong fuzzy compact (resp. fuzzy compact, N-compact). The author also proves that the induced I( L)-fuzzy topological space is ∗-paracompact if and only if the L-fuzzy topological space is ∗-paracompact.

On countably strong fuzzy compact sets in L-fuzzy topological spaces

In this paper, the concept of countably strong fuzzy compact subsets in L-fuzzy topological spaces has been presented by taking strong fuzzy compactness which is due to Lowen (1978) as background. The basic properties of countably strong fuzzy compact subsets have been discussed. Some characterizations of countably strong fuzzy compact subsets have been given by taking the stratum structures of L-fuzzy sets as the point of departure. Also it is pointed out that countably strong fuzzy compactness is an “ L-good extension” of usual countably compactness.

Some results on fuzzy compact spaces

In this paper we examine first the relation between the fuzzy compactness of a fuzzy topology on a fuzzy lattice L and the compactness of two topological spaces ( M, u), ( M, v) defined on the set M of molecules of L. We then investigate the relation between fuzzy compactness and the joint compactness of the bitopological space ( M, u, v).