Investigation of Fuzzy pre m-open Sets and their Applications via Fuzzy Ideal Topological Spaces

In this work, we introduce a new type of fuzzy local function on fuzzy ideal spaces by using the notion of fuzzy pre m-open sets obtained from fuzzy pre-open sets, and explore several properties of them. We show that this given type and fuzzy local function (fuzzy α-local function) are independent each other. Then, we put forward a fresh sort of closure operation via fuzzy pre-m-local functions and apply to generate a fuzzy topology which is finer than original one. Finally, we set up the notion of fuzzy pre-m-compatible inspired by fuzzy pre-m-quasi neighbourhoods and acquire some characterizations and properties of this notion. Additionally, we investigate necessary and sufficient conditions for a set to be closed in the fuzzy topology arising from the closure operation. Through this content, we construct certain illustrative examples to demonstrate the invalidity of some inverse implementations of results.