Some Topological Concepts via Level Subsets of a Fuzzy Subset

Some Topological and Algebraic Properties of α-level Subsets’ Topology of a Fuzzy Subset

“…Furthermore, this also guarantees that every open set which contains µ α0 contains other points which are not in µ α0 but to a certain degree are contained in µ. With this construction, it is also possible to define the fuzzy cluster point of a level set µ αi for any i which will coincide with the definition of the same as given by Onasanya in [20]. In such case we say that an x which to a certain degree belongs to a fuzzy set µ is a fuzzy cluster point of a level subset µ αi of a fuzzy set µ if for every…”

“…Then, U and U β as defined by Onasanya in [20] can be taken respectively as O α k and µ α in which case A α ∩U \{x} = ∅ with β ≤ α is like…”

“…This idea was also followed by Benchalli [2] to obtain some fuzzy topological properties such as α-Hausdorffness, α-connectedness and α-compactness. Onasanya in [20] also introduced and studied some properties such as fuzzy accumulation (or cluster) points of an α-level subset of a fuzzy topological space instead of that of fuzzy cluster set introduced by Chang in [5]. This also makes it easier to avoid fuzzy points.…”