关键词: 模糊逻辑, Lucasiewicz逻辑系统, 多值逻辑代数（MV）, 子代数, 重言式

Abstract: The structures of subalgebras of MV unit interval [[0,1]] and n-valued MV algebra [Ln] with  the relations of tautologies on them are studied intensively. The main results of this paper are as follows: if a subalgebra [M]of MV unit interval [[0,1]] is isomorphism to a subalgebra of MV algebra [Ln], then there exists a positive integer [m] such as [(m-1)|(n-1)] and [M=Lm]; if [M]is a subalgebra of MV unit interval [[0,1]], then [M] is an n-valued MV algebra [Ln], or [M]is a dense subset of [[0,1]] containing [{0,1}]; if positive integer [n-1] can be factored as [(m1-1)(m2-1)?(mt-1)] with positive integers [m1-1,m2-1,?,mt-1] relatively prime in pairs, then MV algebra [Ln] can be generated by subalgebras [Lm1,Lm2,?,Lmt]; [T([0,1])=n=2∞T(Ln)], where [T(M)] is the set of all tautologies on MV-algebra [M].

Key words: fuzzy logic, Lucasiewicz-logic system, algebras of Many-Valued logics（MV）, subalgebra, tautology