In this paper, we present a new type of set called $\Psi_{\Gamma}-C$ by using the operator $\Psi_{\Gamma}$. We investigate relationships these sets with some special which were studied in literature. For instance $\theta$-open set, semi $\theta$-semiopen regular $\theta$-closed set. particular, show that is weaker than Furthermore, prove collection closed under arbitrary union. Finally, obtain ...

In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the ...