A new type of generalized closed set via γ-open set in a fuzzy bitopological space

Resumen

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)  [Tripathy, B. C., & Debnath, S. (2013),   γ-Open sets and γ-Continuous Mappings in Fuzzy Bitopological Spaces, Journal of Intelligence and Fuzzy Systems, 24, 631-635] 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 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 application.

Biografía del autor/a

Birojit Das, National Institute of Technology.
Department of Mathematics.
Baby Bhattacharya, National Institute of Technology.
Department of Mathematics.
Jayasree Chakaraborty, National Institute of Technology.
Department of Mathematics.
Sree Anusha Ganapathiraju, National Institute of Technology.
Department of Mathematics.
Arnab Paul, Techno India.
Department of Mathematics.

Citas

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Publicado
2019-08-14
Cómo citar
[1]
B. Das, B. Bhattacharya, J. Chakaraborty, S. A. Ganapathiraju, y A. Paul, «A new type of generalized closed set via γ-open set in a fuzzy bitopological space», Proyecciones (Antofagasta, En línea), vol. 38, n.º 3, pp. 511-536, ago. 2019.
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