On Fuzzy Generalized $\alpha$-Closed Set and Its Applications

Bayaz Daraby, S. B. Nimse

In this paper, we define and study fuzzy generalized $\alpha$-closed sets and $r$-open sets of a given $L$-fuzzy topological space and prime element $r\in P(L)$ and coprime element $\alpha\in M(L)$. The concept of $L$-fuzzy ropen sets was introduced in [10], and it was proved that all $r$-open sets for $L$-fuzzy topological space form a new $L$-fuzzy topology, which is called stratiform $L$-fuzzy topology. Making use of the fuzzy generalized $\alpha$-closed sets, fuzzy generalized $\alpha$-continuous map is presented.