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We characterize fuzzy Boolean and implicative filters in pseudo BCK algebras, then get the essential equivalent relation between the two fuzzy filters. Based on this, we solve an open problem in pseudo BCK algebras. By constructing the Chinese remainder theorem with respect to filters in distributive lattice of polynomials, a new kind of communication encoding scheme is obtained, and we analyze the security of the scheme.

Solution to open problems on fuzzy filters in logical algebras and secure communication encoding scheme on filters