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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.3 Antofagasta ago. 2019

http://dx.doi.org/10.22199/issn.0717-6279-2019-03-0033 

Articles

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

1National Institute of Technology, Department of Mathematics, Agartala, 799046, India. e-mail: dasbirojit@gmail.com

2National Institute of Technology, Department of Mathematics, Agartala, 799046, India. e-mail: babybhatt75@gmail.com

3National Institute of Technology, Department of Mathematics, Agartala, 799046, India. e-mail: chakrabortyjayasree1@gmail.com

4National Institute of Technology, Department of Mathematics, Agartala, 799046, India. e-mail : sreeanusha17@gmail.com

5 Techno India, Department of Mathematics, Agartala, 799130, India. e-mail : mrarnabpaul87@gmail.com

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.

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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Received: April 2018; Accepted: December 2018

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