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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.2 Antofagasta jun. 2019

http://dx.doi.org/10.4067/S0716-09172019000200237 

Articles

On Fuzzy Λ γ -Sets and their Applications

Baby Bhattacharya1 

Arnab Paul2 

Jayasree Chakraborty3 

1National Institute of Technology, Agartala, 799046, India. e-mail: babybhatt75@gmail.com

2Techno College of Engineering Agartala, Science and Humanities Department, Agartala, 799004, India. e-mail : mrarnabpaul87@gmail.com

3National Institute of Technology, Agartala, 799046, India. e-mail: chakrabortyjaysree1@gmail.com

Abstract

The notion of Λ-fuzzy set was introduced by M. E. EI-Shafei and A. Zakari in 2006 ((20)). We examine some basic properties of it and prove some characterization theorems for the same. The paper presents a new class of fuzzy sets called fuzzy Λγ-sets that includes the class of all fuzzy γ-open sets. It also introduces the notion of fuzzy Vγ-sets as the dual concept of fuzzy Λγ sets to study the spaces constituted by those sets and obtain a completely different structure which is called fuzzy independent Alexandorff space. A stronger form of fuzzy Λb - continuity ((2)) called fuzzy Λγ-continuity is introduced and the relationships are also established with the already existing functions accordingly. Finally, fuzzy Λγ-Generalized closed sets are defined and studied with some of their applications.

Keyword: Fuzzy γ-open set; Fuzzy independent topology; FuzzyΛb-set; Fuzzy Λγ-set; Fuzzy Λb-continuity; Fuzzy Λγ-closed set.

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Received: June 2017; Accepted: March 2019

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