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## Proyecciones (Antofagasta)

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*Print version* ISSN 0716-0917

### Proyecciones (Antofagasta) vol.38 no.2 Antofagasta June 2019

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

Articles

On Fuzzy Λ _{γ} -Sets and their Applications

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

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

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

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 Λ_{γ}-sets that includes the class of all fuzzy γ-open sets. It also introduces the notion of fuzzy V_{γ}-sets as the dual concept of fuzzy Λ_{γ} 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 Λ_{b} - continuity ((^{2})) called fuzzy Λ_{γ}-continuity is introduced and the relationships are also established with the already existing functions accordingly. Finally, fuzzy Λ_{γ}-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