区间集上的格蕴涵代数、FI-代数、MV-代数的研究

Lattice Implication Algebras,FI-algebras,and MV-algebras Based on the Interval Sets

区间集是一个新的重要的研究方向,在近似推理、模糊控制等领域中有着广泛的应用。在区间集上,重新定义了区间蕴涵,构造了格蕴涵代数,讨论了格蕴涵代数的一系列性质。同时在区间集上也重新定义了可换FI-代数和MV-代数,证明了格蕴涵代数、FI-代数和MV-代数3种不同的代数系统是等价的。

The interval sets are new important direction of the research,which have been widely applied in approximate reasoning,fuzzy control,and so on.In the interval sets,the new interval implication（■） was redefined,the lattice implication algebras was reconstructed and its properties were discussed.Meanwhile,commutative FI-algebras and MV-algebras also were redefined in the interval sets.Three different algebraic systems were proved to equivalence,which are lattice implication algebras,commutative FI-algebras and MV-algebras.