$r$-fuzzy regular semi open sets in smooth topological spaces

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 relationship among fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Finally, we have given some counter examples to show that these types of mappings are not equivalent.