ON GENERALIZATION OF S-CLOSEDNESS FOR FUZZY TOPOLOGICAL SPACES THROUGH FUZZY IDEALS, 2014
The paper deals with the concept of fuzzy S-closedness in the generalized setting of a fuzzy topo... more The paper deals with the concept of fuzzy S-closedness in the generalized setting of a fuzzy topological spaces. Fuzzy S-closedness is shown to be a generalization of the well known concept of fuzzy S-closedness defined by D. Coker and A. Haydar Es in 1987. Fuzzy filter-base () is used to characterize the said concept to some extent. Concept of-(finite intersection property modulo) is used to characterize and study the concept of fuzzy Sclosedness for fuzzu extremally disconnected (FED) spaces. Restriction of the notion of fuzzy S-closedness to the arbitrary fuzzy sets in and invariance of the property under suitable maps are also taken into consideration.
In this article semi-open and semi-closed sets on a fuzzy soft topological space are introduced a... more In this article semi-open and semi-closed sets on a fuzzy soft topological space are introduced and some properties have been studied. Fuzzy soft semi closure and fuzzy soft semi interior operators are also introduced and studied. Semi-continuous, semi-open, semi-clsoed and irresolute fuzzy soft functions on a fuzzy soft topological space are introduced and characterized.
This paper deals with the concept of-limit points of crisp subsets of a fuzzy topological space a... more This paper deals with the concept of-limit points of crisp subsets of a fuzzy topological space and the concept of-closed sets in. A special type of crisp subsets (termed as-N-open sets) of a fuzzy topological space is defined as the complement of-closed sets in and a special class of ordinary topological spaces is introduced. This newly defined graded topological spaces (denoted by (N)) are used to study and characterize some fuzzy topological properties such as compactness and other compact-like covering properties and Hausdorffness, connectedness etc.
In this paper, fuzzy AI-set, fuzzy BI-set, fuzzy CI-set, fuzzy I-locally closed set of fuzzy idea... more In this paper, fuzzy AI-set, fuzzy BI-set, fuzzy CI-set, fuzzy I-locally closed set of fuzzy ideal topological spaces are studied and characterized and several results and implications are obtained. We introduced fuzzy strongly b-I-open set. Fuzzy strongly α-I-open set was introduced by A. Selvakumar et al. in 2009 and fuzzy strongly pre-I-open set was introduced by Bin Chen in 2011. We characterized fuzzy strongly α-I-open set in terms fuzzy strongly pre-I-open set and fuzzy strongly b-I-open set and ultimately we obtained a new characterization of fuzzy open set. The aim of this paper is to obtain a new decomposition of fuzzy continuity. With the help of such characterizations we obtained several generalizations of fuzzy continuous functions and finally we obtained a new decomposition of fuzzy continuity in terms of fuzzy strongly α-I-open set and fuzzy AIset. The notions and results given in this paper may lead to some interesting analytical study and research in the arena of Physical Sciences and Mathematical Sciences.
In this paper some fuzzy subsets like fuzzy regular-I-closed set, fuzzy-set, fuzzy-locally closed... more In this paper some fuzzy subsets like fuzzy regular-I-closed set, fuzzy-set, fuzzy-locally closed set, fuzzy-set of fuzzy ideal topological spaces are studied and characterized. We also characterized-codense fuzzy ideals in terms of fuzzy-set, fuzzy regular-I-closed set, fuzzy-locally closed set and we obtain a decomposition of fuzzy continuity.
The paper deals with the concept of fuzzy S-closedness in the generalized setting of a fuzzy topo... more The paper deals with the concept of fuzzy S-closedness in the generalized setting of a fuzzy topological spaces. Fuzzy S-closedness is shown to be a generalization of the well known concept of fuzzy S-closedness defined by D. Coker and A. Haydar Es in 1987. Fuzzy filter-base () is used to characterize the said concept to some extent. Concept of-(finite intersection property modulo) is used to characterize and study the concept of fuzzy Sclosedness for fuzzu extremally disconnected (FED) spaces. Restriction of the notion of fuzzy S-closedness to the arbitrary fuzzy sets in and invariance of the property under suitable maps are also taken into consideration.
In this paper, fuzzy α-I-open set, fuzzy semi-I-open set, fuzzy pre-I-open set, fuzzy A I-set, fu... more In this paper, fuzzy α-I-open set, fuzzy semi-I-open set, fuzzy pre-I-open set, fuzzy A I-set, fuzzy B I-set, fuzzy C I-set, fuzzy regular-I-closed set, fuzzy I-locally closed set of fuzzy ideal topological spaces are studied and characterized and several results and implications are obtained. We introduced fuzzy S I-set. Ultimately, we obtained some characterizations of fuzzy open set. With the help of such characterization we finally introduced decomposition of fuzzy continuous function in terms of fuzzy α-I-open set and fuzzy A I-set and fuzzy S I-set.
This paper deals with the concept of fuzzy I b-compactness in the generalized setting of a fuzzy ... more This paper deals with the concept of fuzzy I b-compactness in the generalized setting of a fuzzy topological space X. The concept of fuzzy b-compact topological space was introduced by G. Balasubramanian in 1997. Fuzzy I b-compactness is shown to be a generalization of the concept of fuzzy b-compactness. Fuzzy filter-base (ffb) is used to characterize the said concept to some extent. Concept of-I FIP (finite intersection property modulo I) is used to characterize and study I b-compactness for fuzzy topological spaces. Restriction of the notion of fuzzy I b-compactness to the arbitrary fuzzy sets in X and invariance of the property under suitable maps are also taken into consideration. The concept of fuzzy I b-closed spaced is also introduced.
In this article semi-open and semi-closed sets on a fuzzy soft topological space are introduced a... more In this article semi-open and semi-closed sets on a fuzzy soft topological space are introduced and some properties have been studied. Fuzzy soft semi closure and fuzzy soft semi interior operators are also introduced and studied. Semi-continuous, semi-open, semi-clsoed and irresolute fuzzy soft functions on a fuzzy soft topological space are introduced and characterized.
In this paper some fuzzy subsets like fuzzy regular-I-closed set, fuzzy-set, fuzzy-locally closed... more In this paper some fuzzy subsets like fuzzy regular-I-closed set, fuzzy-set, fuzzy-locally closed set, fuzzy-set of fuzzy ideal topological spaces are studied and characterized. We also characterized-codense fuzzy ideals in terms of fuzzy-set, fuzzy regular-I-closed set, fuzzy-locally closed set and we obtain a decomposition of fuzzy continuity.
This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft clo... more This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft closure and fuzzy soft interior of a fuzzy soft set are studied and investigated. Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.
This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft clo... more This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft closure and fuzzy soft interior of a fuzzy soft set are studied and investigated. Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.
International Journal of Mathematical Archive, 2014
T he paper deals with the concept of fuzzy S –closedness in the generalized setting of a fuzzy to... more T he paper deals with the concept of fuzzy S –closedness in the generalized setting of a fuzzy topological spaces . Fuzzy S –closedness is shown to be a generalization of the well known concept of fuzzy S–closedness defined by D. Coker and A. Haydar Es in 1987. Fuzzy filter-base ( ) is used to characterize the said concept to some extent. Concept of – (finite intersection property modulo ) is used to characterize and study the concept of fuzzy S –closedness for fuzzu extremally disconnected (FED) spaces. Restriction of the notion of fuzzy S –closedness to the arbitrary fuzzy sets in and invariance of the property under suitable maps are also taken into consideration.
In this article, some open-like fuzzy soft sets such as fuzzy soft semi-open set, fuzzy soft preo... more In this article, some open-like fuzzy soft sets such as fuzzy soft semi-open set, fuzzy soft preopen set, fuzzy soft α-open set and corresponding variants of fuzzy soft continuous functions are introduced and discussed. Some other variants of fuzzy soft sets such as fuzzy soft semi-preclosed set, fuzzy soft t-set, fuzzy soft α*-set, fuzzy soft regular open set, fuzzy soft B-set, fuzzy soft C-set and fuzzy soft D(α)-set are defined and some properties of these sets are studied and investigated. Some continuouslike functions are introduced and we obtained some decomposition of fuzzy soft continuity.
The concept of compactness is one of the central and important concepts of paramount interest to ... more The concept of compactness is one of the central and important concepts of paramount interest to topologists and it seems to be the most celebrated type among all the covering properties. In this paper the concept of compactness of fuzzy soft topological spaces is introduced and characterized in terms of finite intersection property (FIP) and in terms of fuzzy soft mappings. This concept is also generalized by introducing the concept of fuzzy soft semi-compact topological spaces. Invariance of the property under suitable maps is also taken into consideration.
This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft clo... more This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft closure and fuzzy soft interior of a fuzzy soft set are studied and investigated. Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.
Journal of Mathematical and Computational Science, Jan 5, 2014
The concept of compactness is one of the central and important concepts of paramount interest to ... more The concept of compactness is one of the central and important concepts of paramount interest to topologists and it seems to be the most celebrated type among all the covering properties. In this paper the concept of compactness of fuzzy soft topological spaces is introduced and characterized in terms of finite intersection property (FIP) and in terms of fuzzy soft mappings. This concept is also generalized by introducing the concept of fuzzy soft semi-compact topological spaces. Invariance of the property under suitable maps is also taken into consideration.
ON GENERALIZATION OF S-CLOSEDNESS FOR FUZZY TOPOLOGICAL SPACES THROUGH FUZZY IDEALS, 2014
The paper deals with the concept of fuzzy S-closedness in the generalized setting of a fuzzy topo... more The paper deals with the concept of fuzzy S-closedness in the generalized setting of a fuzzy topological spaces. Fuzzy S-closedness is shown to be a generalization of the well known concept of fuzzy S-closedness defined by D. Coker and A. Haydar Es in 1987. Fuzzy filter-base () is used to characterize the said concept to some extent. Concept of-(finite intersection property modulo) is used to characterize and study the concept of fuzzy Sclosedness for fuzzu extremally disconnected (FED) spaces. Restriction of the notion of fuzzy S-closedness to the arbitrary fuzzy sets in and invariance of the property under suitable maps are also taken into consideration.
In this article semi-open and semi-closed sets on a fuzzy soft topological space are introduced a... more In this article semi-open and semi-closed sets on a fuzzy soft topological space are introduced and some properties have been studied. Fuzzy soft semi closure and fuzzy soft semi interior operators are also introduced and studied. Semi-continuous, semi-open, semi-clsoed and irresolute fuzzy soft functions on a fuzzy soft topological space are introduced and characterized.
This paper deals with the concept of-limit points of crisp subsets of a fuzzy topological space a... more This paper deals with the concept of-limit points of crisp subsets of a fuzzy topological space and the concept of-closed sets in. A special type of crisp subsets (termed as-N-open sets) of a fuzzy topological space is defined as the complement of-closed sets in and a special class of ordinary topological spaces is introduced. This newly defined graded topological spaces (denoted by (N)) are used to study and characterize some fuzzy topological properties such as compactness and other compact-like covering properties and Hausdorffness, connectedness etc.
In this paper, fuzzy AI-set, fuzzy BI-set, fuzzy CI-set, fuzzy I-locally closed set of fuzzy idea... more In this paper, fuzzy AI-set, fuzzy BI-set, fuzzy CI-set, fuzzy I-locally closed set of fuzzy ideal topological spaces are studied and characterized and several results and implications are obtained. We introduced fuzzy strongly b-I-open set. Fuzzy strongly α-I-open set was introduced by A. Selvakumar et al. in 2009 and fuzzy strongly pre-I-open set was introduced by Bin Chen in 2011. We characterized fuzzy strongly α-I-open set in terms fuzzy strongly pre-I-open set and fuzzy strongly b-I-open set and ultimately we obtained a new characterization of fuzzy open set. The aim of this paper is to obtain a new decomposition of fuzzy continuity. With the help of such characterizations we obtained several generalizations of fuzzy continuous functions and finally we obtained a new decomposition of fuzzy continuity in terms of fuzzy strongly α-I-open set and fuzzy AIset. The notions and results given in this paper may lead to some interesting analytical study and research in the arena of Physical Sciences and Mathematical Sciences.
In this paper some fuzzy subsets like fuzzy regular-I-closed set, fuzzy-set, fuzzy-locally closed... more In this paper some fuzzy subsets like fuzzy regular-I-closed set, fuzzy-set, fuzzy-locally closed set, fuzzy-set of fuzzy ideal topological spaces are studied and characterized. We also characterized-codense fuzzy ideals in terms of fuzzy-set, fuzzy regular-I-closed set, fuzzy-locally closed set and we obtain a decomposition of fuzzy continuity.
The paper deals with the concept of fuzzy S-closedness in the generalized setting of a fuzzy topo... more The paper deals with the concept of fuzzy S-closedness in the generalized setting of a fuzzy topological spaces. Fuzzy S-closedness is shown to be a generalization of the well known concept of fuzzy S-closedness defined by D. Coker and A. Haydar Es in 1987. Fuzzy filter-base () is used to characterize the said concept to some extent. Concept of-(finite intersection property modulo) is used to characterize and study the concept of fuzzy Sclosedness for fuzzu extremally disconnected (FED) spaces. Restriction of the notion of fuzzy S-closedness to the arbitrary fuzzy sets in and invariance of the property under suitable maps are also taken into consideration.
In this paper, fuzzy α-I-open set, fuzzy semi-I-open set, fuzzy pre-I-open set, fuzzy A I-set, fu... more In this paper, fuzzy α-I-open set, fuzzy semi-I-open set, fuzzy pre-I-open set, fuzzy A I-set, fuzzy B I-set, fuzzy C I-set, fuzzy regular-I-closed set, fuzzy I-locally closed set of fuzzy ideal topological spaces are studied and characterized and several results and implications are obtained. We introduced fuzzy S I-set. Ultimately, we obtained some characterizations of fuzzy open set. With the help of such characterization we finally introduced decomposition of fuzzy continuous function in terms of fuzzy α-I-open set and fuzzy A I-set and fuzzy S I-set.
This paper deals with the concept of fuzzy I b-compactness in the generalized setting of a fuzzy ... more This paper deals with the concept of fuzzy I b-compactness in the generalized setting of a fuzzy topological space X. The concept of fuzzy b-compact topological space was introduced by G. Balasubramanian in 1997. Fuzzy I b-compactness is shown to be a generalization of the concept of fuzzy b-compactness. Fuzzy filter-base (ffb) is used to characterize the said concept to some extent. Concept of-I FIP (finite intersection property modulo I) is used to characterize and study I b-compactness for fuzzy topological spaces. Restriction of the notion of fuzzy I b-compactness to the arbitrary fuzzy sets in X and invariance of the property under suitable maps are also taken into consideration. The concept of fuzzy I b-closed spaced is also introduced.
In this article semi-open and semi-closed sets on a fuzzy soft topological space are introduced a... more In this article semi-open and semi-closed sets on a fuzzy soft topological space are introduced and some properties have been studied. Fuzzy soft semi closure and fuzzy soft semi interior operators are also introduced and studied. Semi-continuous, semi-open, semi-clsoed and irresolute fuzzy soft functions on a fuzzy soft topological space are introduced and characterized.
In this paper some fuzzy subsets like fuzzy regular-I-closed set, fuzzy-set, fuzzy-locally closed... more In this paper some fuzzy subsets like fuzzy regular-I-closed set, fuzzy-set, fuzzy-locally closed set, fuzzy-set of fuzzy ideal topological spaces are studied and characterized. We also characterized-codense fuzzy ideals in terms of fuzzy-set, fuzzy regular-I-closed set, fuzzy-locally closed set and we obtain a decomposition of fuzzy continuity.
This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft clo... more This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft closure and fuzzy soft interior of a fuzzy soft set are studied and investigated. Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.
This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft clo... more This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft closure and fuzzy soft interior of a fuzzy soft set are studied and investigated. Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.
International Journal of Mathematical Archive, 2014
T he paper deals with the concept of fuzzy S –closedness in the generalized setting of a fuzzy to... more T he paper deals with the concept of fuzzy S –closedness in the generalized setting of a fuzzy topological spaces . Fuzzy S –closedness is shown to be a generalization of the well known concept of fuzzy S–closedness defined by D. Coker and A. Haydar Es in 1987. Fuzzy filter-base ( ) is used to characterize the said concept to some extent. Concept of – (finite intersection property modulo ) is used to characterize and study the concept of fuzzy S –closedness for fuzzu extremally disconnected (FED) spaces. Restriction of the notion of fuzzy S –closedness to the arbitrary fuzzy sets in and invariance of the property under suitable maps are also taken into consideration.
In this article, some open-like fuzzy soft sets such as fuzzy soft semi-open set, fuzzy soft preo... more In this article, some open-like fuzzy soft sets such as fuzzy soft semi-open set, fuzzy soft preopen set, fuzzy soft α-open set and corresponding variants of fuzzy soft continuous functions are introduced and discussed. Some other variants of fuzzy soft sets such as fuzzy soft semi-preclosed set, fuzzy soft t-set, fuzzy soft α*-set, fuzzy soft regular open set, fuzzy soft B-set, fuzzy soft C-set and fuzzy soft D(α)-set are defined and some properties of these sets are studied and investigated. Some continuouslike functions are introduced and we obtained some decomposition of fuzzy soft continuity.
The concept of compactness is one of the central and important concepts of paramount interest to ... more The concept of compactness is one of the central and important concepts of paramount interest to topologists and it seems to be the most celebrated type among all the covering properties. In this paper the concept of compactness of fuzzy soft topological spaces is introduced and characterized in terms of finite intersection property (FIP) and in terms of fuzzy soft mappings. This concept is also generalized by introducing the concept of fuzzy soft semi-compact topological spaces. Invariance of the property under suitable maps is also taken into consideration.
This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft clo... more This paper deals with some structural properties of fuzzy soft topological spaces. Fuzzy soft closure and fuzzy soft interior of a fuzzy soft set are studied and investigated. Fuzzy soft exterior and fuzzy soft boundary of a fuzzy soft set are introduced and some properties related to these structures are established.
Journal of Mathematical and Computational Science, Jan 5, 2014
The concept of compactness is one of the central and important concepts of paramount interest to ... more The concept of compactness is one of the central and important concepts of paramount interest to topologists and it seems to be the most celebrated type among all the covering properties. In this paper the concept of compactness of fuzzy soft topological spaces is introduced and characterized in terms of finite intersection property (FIP) and in terms of fuzzy soft mappings. This concept is also generalized by introducing the concept of fuzzy soft semi-compact topological spaces. Invariance of the property under suitable maps is also taken into consideration.
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