On Weak and Strong Forms of Fuzzy Soft Open Sets

Abstract

We introduce and examined some basic properties of fuzzy soft α-open (closed) sets in fuzzy soft topological spaces. Fuzzy soft pre-open (closed) sets are also defined and discussed. We also initiate and explore fuzzy soft neighborhood at fuzzy soft point. Some properties of fuzzy soft neighborhood system, fuzzy soft basic neighborhood and fuzzy soft neighborhood (nbd) base at fuzzy soft point are studied. Moreover, we define and study fuzzy soft regular open (closed) sets. We analyze the relationship between these notions by providing examples and counter examples.

Keywords

• Fuzzy soft sets
• Fuzzy soft topology
• Fuzzy soft α-open (closed)
• Fuzzy soft pre-open(closed)
• Fuzzy soft neighborhood
• Fuzzy soft point
• Fuzzy soft regular-open (closed)