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

Abstract

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.

Keywords

• fuzzy $beta$-open
• pseudo regular open fuzzy topology
• $ps$-$ro$ $beta$-open(closed) fuzzy sets
• $ps$-$ro$ fuzzy $beta$-continuity
• $ps$-$ro$ fuzzy $beta$-open(closed) function