完备格上基于t算子的直觉模糊粗糙集模型

Intuitionistic fuzzy rough set models on the complete lattice based on the t-norm

摘要: 基于对偶三角模,将直觉模糊粗糙集模型在完备格上进行统一处理:首先在完备格上引入非算子的概念,定义和讨论了完备格上基于t算子的直觉模糊集及其运算法则;讨论了完备格上基于t算子的对偶三角模剩余蕴涵及其相互转化关系;在讨论完备格上基于t算子的直觉模糊集的对偶三角模TS隶属度和非隶属度表示的基础上,给出了完备格上基于t算子的直觉模糊集对应的剩余蕴涵之隶属度和非隶属度计算公式;最后,在定义完备格上基于t算子相似关系的基础上,定义和刻画了完备格上基于t算子的直觉模糊粗糙集模型.

Abstract: Based on dual triangle norms,the intuitionistic fuzzy rough set models were investigated.Firstly,the concept of negation operator on a complete lattice was introduced,and the intuitionistic fuzzy set based on the t-norm on the complete lattice and its arithmetic operations were defined and discussed.Secondly,The TS membership degree and TS non-membership degree of intuitionistic fuzzy sets of dual triangular norms based on t-norm on the complete lattice were defined and characterized.Finally,on the basis of similarity relation based on the t-norm on the complete lattice,intuitionistic fuzzy rough set models on the complete lattice based on the t-norm were defined and studied.