Solution to Open Problems on Fuzzy Filters in Logical algebras and Secure Communication Encoding Scheme on Filters

Abstract

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.