A new type of generalized closed set via γ-open set in a fuzzy bitopological space
Abstract This paper aims to present the notion of (i, j)*-fuzzy γ-open set in a fuzzy bitopological space as a parallel form of (i, j)-fuzzy γ-open set due to Tripathy and Debnath (2013) [17] and show that both of them are independent concepts. Then we extend our study to (i, j)*-g...
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2019
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oai:scielo:S0716-091720190003005112019-08-28A new type of generalized closed set via γ-open set in a fuzzy bitopological spaceDas,BirojitBhattacharya,BabyChakraborty,JayasreeSree Anusha,G.Paul,Arnab (i, j)*-fuzzy γ-open set (i, j)*-generalized fuzzy γ-closed set (i, j)*-γ-generalized fuzzy closed set (i, j)*-generalized fuzzy γ-continuous function (i, j)*-generalized fuzzy γ-irresolute function Abstract This paper aims to present the notion of (i, j)*-fuzzy γ-open set in a fuzzy bitopological space as a parallel form of (i, j)-fuzzy γ-open set due to Tripathy and Debnath (2013) [17] and show that both of them are independent concepts. Then we extend our study to (i, j)*-generalized fuzzy γ-closed set and (i, j)*-γ-generalized fuzzy closed set. We show that (i, j)*-γ-generalized fuzzy closed set and (i, j)*-generalized fuzzy γ-closed set are also independent of each other in nature. Though every (i, j)*-fuzzy γ-closed set is a (i, j)*-generalized fuzzy γ-closed set but with (i, j)*-γ-generalized fuzzy closed set, the same relation is not linear. Similarly though every (i, j)*-fuzzy closed set is (i, j)*-γ-generalized fuzzy closed set but it is independent to (i, j)*-generalized fuzzy γ-closed set. Various properties related to (i, j)*-generalized fuzzy γ-closed set are also studied. Finally, (i, j)*-generalized fuzzy γ-continuous function and (i, j)*-generalized fuzzy γ-irresolute functions are introduced and interrelationships among them are established. We characterized these functions in different directions for different applications.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.38 n.3 20192019-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300511en10.22199/issn.0717-6279-2019-03-0033 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
(i, j)*-fuzzy γ-open set (i, j)*-generalized fuzzy γ-closed set (i, j)*-γ-generalized fuzzy closed set (i, j)*-generalized fuzzy γ-continuous function (i, j)*-generalized fuzzy γ-irresolute function |
| spellingShingle |
(i, j)*-fuzzy γ-open set (i, j)*-generalized fuzzy γ-closed set (i, j)*-γ-generalized fuzzy closed set (i, j)*-generalized fuzzy γ-continuous function (i, j)*-generalized fuzzy γ-irresolute function Das,Birojit Bhattacharya,Baby Chakraborty,Jayasree Sree Anusha,G. Paul,Arnab A new type of generalized closed set via γ-open set in a fuzzy bitopological space |
| description |
Abstract This paper aims to present the notion of (i, j)*-fuzzy γ-open set in a fuzzy bitopological space as a parallel form of (i, j)-fuzzy γ-open set due to Tripathy and Debnath (2013) [17] and show that both of them are independent concepts. Then we extend our study to (i, j)*-generalized fuzzy γ-closed set and (i, j)*-γ-generalized fuzzy closed set. We show that (i, j)*-γ-generalized fuzzy closed set and (i, j)*-generalized fuzzy γ-closed set are also independent of each other in nature. Though every (i, j)*-fuzzy γ-closed set is a (i, j)*-generalized fuzzy γ-closed set but with (i, j)*-γ-generalized fuzzy closed set, the same relation is not linear. Similarly though every (i, j)*-fuzzy closed set is (i, j)*-γ-generalized fuzzy closed set but it is independent to (i, j)*-generalized fuzzy γ-closed set. Various properties related to (i, j)*-generalized fuzzy γ-closed set are also studied. Finally, (i, j)*-generalized fuzzy γ-continuous function and (i, j)*-generalized fuzzy γ-irresolute functions are introduced and interrelationships among them are established. We characterized these functions in different directions for different applications. |
| author |
Das,Birojit Bhattacharya,Baby Chakraborty,Jayasree Sree Anusha,G. Paul,Arnab |
| author_facet |
Das,Birojit Bhattacharya,Baby Chakraborty,Jayasree Sree Anusha,G. Paul,Arnab |
| author_sort |
Das,Birojit |
| title |
A new type of generalized closed set via γ-open set in a fuzzy bitopological space |
| title_short |
A new type of generalized closed set via γ-open set in a fuzzy bitopological space |
| title_full |
A new type of generalized closed set via γ-open set in a fuzzy bitopological space |
| title_fullStr |
A new type of generalized closed set via γ-open set in a fuzzy bitopological space |
| title_full_unstemmed |
A new type of generalized closed set via γ-open set in a fuzzy bitopological space |
| title_sort |
new type of generalized closed set via γ-open set in a fuzzy bitopological space |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2019 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172019000300511 |
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