基于对偶三角模的直觉模糊粗糙集模型

Intuitionistic fuzzy rough sets models based on dual triangular norms

针对直觉模糊集同时考虑隶属度与非隶属度两方面的信息,使得在处理不确定信息时比传统的模糊集具有更好的表达能力和灵活性等特点,注意到无论是直觉模糊集的四则运算,还是直觉模糊集的比较排序,其隶属度和非隶属度的运算表现为一定意义下的一组对偶三角模的事实,将直觉模糊粗糙集模型在对偶三角模意义下进行了统一处理.讨论了对偶三角模剩余蕴涵及其相互转化关系;在讨论针对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,给出了针对直觉模糊集且与之对应的剩余蕴涵的隶属度和非隶属度计算公式;同时,在定义二元直觉模糊关系的基础上定义和刻画了基于对偶三角模直觉模糊粗糙集模型.

Since intuitionistic fuzzy sets could provide the information on the membership degree and the nonmembership degree, it should have better expression and flexibility than traditional fuzzy sets in processing uncertain information data. Note that the operations of the membership degree and the non-membership degree could be expressed as a couple of dual triangular norms in the arithmetic operations of intuitionistic fuzzy sets. The intuitionistic fuzzy rough sets models were investigated based on the dual triangular norms in this paper. The dual triangular norms and its residual implications were discussed and represented. The TS membership degree and TS non-membership degree of intuitionistic fuzzy sets based on dual triangular norms were defined and characterized. Intuitionistic fuzzy rough sets models based in dual triangular norms were defined and studied.