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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 -ideals and -filters of fuzzy lattices and characterize it by using its support and its level set, and we propose a new notion of fuzzy -lattices and fuzzy distributive -lattices.
About the author
Ivan Mezzomo received the Ph.D. degree in computer science from the UFRN, Brazil, in 2013. In 2010, he became an Assistant Professor with the UFERSA, Brazil. Benjamín Bedregal received the Ph.D. degree in computer sciences from the UFPE, in 1996. In 1996, he became an Assistant Professor with the UFRN, Brazil.
