Abstract
The Kleene's fuzzy logic is repersented by Kleene algebra and its generalization is De Morgan algebra. In this paper, we present basic properties of Kleene algebra and De Morgan algebra, and various resalts on Kleene algebra, De Morgan algebra with centers. The necessary and sufficient condition for a distributive lattice to be a Kleene algebra (De Morgan algebra) is given. We also study the structure of the Kleene algebra (De Morgan algebra).
