The aim of this work is to introduce certain types of fuzzy closed sets such as fuzzy regular closed set, fuzzy – closed set, fuzzy - closed, fuzzy – closed set and fuzzy – closed set. We studied the relation among them and some fundamental properties of these sets. Also we introduced and studied fuzzy regular open set, fuzzy – open set, fuzzy - open set, fuzzy – open set, also we gave the relation between them and some fundamental properties of those sets. Also we introduce the concept of a and study some properties of this fuzzy set. We depended a fuzzy topology which is defined on a fuzzy set instead of a crisp set when we defined these sets
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