Abstract
In this paper, based on complete residuated lattices, the properties of fuzzy $$Z_{L}$$ -continuous posets and fuzzy $$Z_{L}$$ -algebraic posets are investigated. Then we show that the set of fuzzy $$Z_{L}$$ -ideals on the set of all compact elements of a fuzzy $$Z_{L}$$ -algebraic poset is a fuzzy $$Z_{L}$$ -closure system. Also, we prove that the image of a (strongly) fuzzy $$Z_{L}$$ -continuous poset under a fuzzy $$Z_{L}$$ -morphism is (strongly) fuzzy $$Z_{L}$$ -continuous.
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