Abstract:

Regular residuated lattices and WBR₀-algebras are investigated in depth. The relationship between WBR₀-algebras and other logic algebras is made  clearer and more definite than before. The main results of this paper are as follows: (1) It is proved that regular residuated lattices and WBR0algebras are the same algebraic structure. (2) The connection among WBR₀-algebras with other classical logic algebras is given by the network, through which the roles of WBR₀-algebras are explained. (3) The difference between WBR₀-algebras and other logic algebras is revealed by constructing a special WBR₀-algebra.

Key words:  fuzzy logic; logic algebra; regular residuated lattice; WBR₀-algebra; BL-algebra