Abstract
This led several authors to investigate the closure systems and the closure operators in the framework of fuzzy set theory. The resulting researches give an elegant and powerful treatment of notions such as those of fuzzy Ž w x subalgebras, necessity measures, and envelopes for example, see 1]4 and w x. 11 . Ž . Ž . Let S be any set, and denote by P S and F S the class of the subsets and the class of the fuzzy subsets of S, respectively. In this paper we propose an ‘‘extension principle’’ enabling us to extend any classical Ž . Ž . Ž . Ž . operator J: P S a P S to an operator J*: F S a F S in such a way that J* is a closure operator if and only if J is a closure operator. Also, we
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