Neutrosophic n-Valued Refined Sets and Topologies

Abstract

In n-Valued refined logic truth value T can be split into many types of truths: T1, T2, ..., Tp and
I into many types of indeterminacies: I1, I2, ..., Ir and F into many types of falsities: F1, F2, ..., Fs, where p, r
and s are integers greater than 1, and p + r + s = n. Importance of n-valued refined logic and sets appeared in
different applications specially in medical diagnosis. In this paper we post a condition on neutrosophic n-valued
refined sets to make them functional to be applied in different mathematical branches. We define and study
n-valued refined topological spaces. We defined neutrosophic n-valued refined α-open, β-open, pre-open and
semi-open sets and studied their properties. We constructed different counter examples to clarify the relations
between these different types of neutrosophic n-valued refined generalized open sets