Abstract: In order to provide the algebraic basis of intuitionistic fuzzy reasoning, the basic theory of regular intuitionistic lattices is preliminarily established.By using the left continuous triangular module on the unit interval0, 1, the concept of the intuitional triangular module and its accompanying regular intuitionistic implication operator is introduced, and their properties are studied with the relationships between the intuitionistic triangular modules and regular intuitionistic implication operators being revealed.