VAGUE BI-IDEAL OF A Γ-NEAR RING
S. RAGAMAYI *
K L University, Vaddeswaram, Guntur, Andhra Pradesh, India.
J. MADHUSUDHANA RAO
Vijaya Engineering College, Ammapalem, Khammam, Telengana, India.
T. ESWARLAL
K L University, Vaddeswaram, Guntur, Andhra Pradesh, India.
Y. BHARGAVI
K L University, Vaddeswaram, Guntur, Andhra Pradesh, India.
*Author to whom correspondence should be addressed.
Abstract
In this article, we introduce and study the concept of a vague bi-ideal of a 
Γ-Near ring and study various properties of it. We prove that a vague set A is vague Bi-ideal of a Γ-Near ring M if and only if the vague cut A(α,β) is a Bi-ideal of M. Further, we prove that homomorphic image and inverse homomorphic image of a vague Bi-ideal of M is also a vague Bi-ideal of M. Also, we prove the characteristic set of S, δS is a vague bi-ideal of M if and only if S is a bi-ideal of M. Further, we prove intersection of two vague bi-ideals is also a vague bi-ideal of M.
Keywords: Vague set, Vague cut, Vague characteristic set, Vague ideal, vague Bi-ideal;, Nearring