区间值模糊集上格蕴涵代数的构造研究

Research on Construction of the Lattice Implication Algebras Based on the Interval-valued Fuzzy Sets

区间值模糊集合是处理不确定、不完全信息的重要基础理论,格蕴涵代数是区间值模糊集上一个重要的研究方向。文章是在区间值模糊集合上,给出了区间补、区间伪补和区间蕴涵三个运算的概念,证明了〈I[0,1],■,■,c,*〉是有余格。与此同时,在区间值模糊集上重新构造了格蕴涵代数(I[0,1],■,■,c,*,■),且讨论了该格蕴涵代数的一些性质。

The interval-valued fuzzy sets is an important basic theory for dealing with uncertainty,incompleteness information.The Lattice Implication Algebras is an important research direction in the internal-valued fuzzy sets.In this paper,the operations are redefined in the interval-valued fuzzy sets,which are the interval complement,the interval pseudo-complement and the interval implication.Furthermore,algebras system 〈I,■,■,c,＊〉 is proved complemented lattice.At the same time,the Lattice Implication Algebras（I,■,■,c,＊,■）is reconstructed in the internal-valued fuzzy sets,and it＇s properties are discussed.