Neutrosophic n-Valued Refined Sets and Topologies

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 © 2023, Neutrosophic Sets and Systems.All Rights Reserved.