On Fuzzy Ideals and Fuzzy Filters of Fuzzy Lattices

Using the fuzzy lattices defined by Chon we define fuzzy homomorphism between fuzzy lattices the operations of product collapsed sum lifting opposite interval and intuitionistic on bounded fuzzy lattices. We define ideals and filters of fuzzy lattices and concepts in the same way as in their characterization in terms of level and support sets. Moreover we introduce a new notion of fuzzy ideals and fuzzy filters for fuzzy lattices and define types of fuzzy ideals and fuzzy filters that generalize usual types of ideals and filters of lattices such as principal ideals proper ideals prime ideals and maximal ideals. We also introduce the notion of α-ideals and α-filters of fuzzy lattices and characterize it by using its support and its level set and we propose a new notion of fuzzy α-lattices and fuzzy distributive α-lattices.