On Two Types of Fuzzy Closed Sets

摘要

Various concepts related to the category of fuzzy closure spaces have been introduced, and relations among them are studied by several authors [4-8]. In this paper, we introduce the weak fuzzy closure operators which need not be closed under unions, showing that many concepts and properties of the category of closure space (FCS) can be proved without additional hypothesis. Initial structures of weak fuzzy closure spaces are obtained. Two notions of closed fuzzy sets, one in terms of fuzzy sets, the other in terms of fuzzy points, are introduced. The interrelations between these two notions are studied, provided with some counterexamples.