模糊等价关系下的犹豫模糊粗糙集及其应用

HESITANT FUZZY ROUGH SET BASED ON SIMILARITY AND ITS APPLICATION

首先通过对长度不同的犹豫模糊元进行补齐来定义犹豫模糊集新的交并运算,在Pawlak近似空间中利用新的运算建立粗糙犹豫模糊集模型;然后将Pawlak近似空间推广到一般犹豫模糊近似空间,利用犹豫模糊元间的相似度获得犹豫模糊近似空间中对象间的模糊关系矩阵,再利用模糊集的传递闭包法将模糊相似矩阵转化成模糊等价矩阵,在此基础上建立犹豫模糊信息系统中的粗糙集模型,研究犹豫模糊信息系统的属性约简。最后通过一个算例来说明犹豫模糊信息系统的属性约简方法。

Firstly, the hesitant fuzzy sets with different lengths are complemented to define the new intersection operation of hesitant fuzzy sets. The new operation is used to establish the rough hesitant fuzzy set model in Pawlak approximation space. Furthermore, the Pawlak approximation space is extended to the general hesitant fuzzy approximation Space, using the similarity between hesitant fuzzy elements to obtain the fuzzy relation matrix between objects in hesitant fuzzy approximation space, and then transform the fuzzy similar matrix into fuzzy equivalent matrix by using the transitive closure method of fuzzy set, and establish a rough set model in hesitant fuzzy information system on this basis to study the attribute reduction of hesitant fuzzy information systems. And an example is given to illustrate the attribute reduction method of hesitant fuzzy information system.