Study on the Solutions of Inequalites in the Lattice Implication Algebra

Abstract: Two calsses of inequalities are studied in the lattice implication algebra. The necessary and sufficient conditions for the existence of solutions for the inequalities were put under discussion respectively, based on which the detailed solution sets are given and the fact is confirmed that the solution sets of the two calsses of inequalities are a convex sub-lattice and a sub-lattice of L, respectively.