EQ-代数的模糊滤子粗糙性研究

Study on the Roughness of Fuzzy Filter on EQ-algebra

EQ-代数作为一种逻辑代数,它与剩余格密切相关,但EQ-代数在本质上对研究模糊逻辑有十分重要的意义。文章运用水平截集的方法将EQ-代数模糊化、粗糙化,由于EQ-代数模糊前滤子理论和粗糙性理论是两种特殊的不确定性理论,所以通过ΕQ-代数滤子的关系,将模糊化可分EQ-代数准滤子、素准滤子,得到可分ΕQ-代数模糊准滤子、素模糊准滤子的概念,同时也得到了模糊准滤子与素模糊准滤子运算之间的关系。

EQ-algebra,a logical algebra,is closely connected with the residual lattice. It is important for the study of classical logic and fuzzy logic in nature. The paper studies how to make EQ-algebra fuzzified and roughened by taking use of the level cut set.Since fuzzy prefilter theory and rough theory are two different theories with uncertainty,fuzzification can be divided into filter and prime prefilter by using the EQ-algebra filter,and thus we get their concepts,as well as the relationships among them.