Some kinds of falling fuzzy filters of lattice implication algebras

In this paper, the concepts of falling fuzzy (implicative, associative) filters of lattice implication algebras based on the theory of falling shadows and fuzzy sets are presented at first. And then the relations between fuzzy (implicative, associative) filters and falling fuzzy (implicative, associative) filters are provided. In particular, we put forward an open question on a kind of falling fuzzy filters of lattice implication algebras. Finally, we apply falling fuzzy inference relations to lattice implication algebras and obtain some related results.

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