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Proyecciones (Antofagasta)

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DAS, Birojit et al. A new type of generalized closed set via γ-open set in a fuzzy bitopological space. Proyecciones (Antofagasta) [online]. 2019, vol.38, n.3, pp.511-536. ISSN 0716-0917.

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.

Keywords : (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.

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