$ps-ro$ $\beta$-Open (Closed) Fuzzy Sets and Related Fuzzy Function and Continuity

In this paper, the  notion of $ps-ro$ $\beta$-open (closed) fuzzy sets on a fuzzy topological space($fts$) has been introduced as a new tool to study $fts$, the properties of these sets are investigated and shown to be unrelated to the common concept of fuzzy $\beta$-open (closed) sets. Based on these fuzzy sets, $ps-ro$ fuzzy $\beta$-continuity and $ps-ro$ fuzzy $\beta$-open (closed) functions are proposed and they are also found to be different from the idea of fuzzy $\beta$-continuous and fuzzy $\beta$-open (closed) functions, respectively. Further, their  characterizations and relationships with existing allied concepts are investigated.