基于区间值模糊剩余蕴含算子的广义区间值模糊粗糙集模型

Generalized Interval-valued Fuzzy Rough Sets Based on the Interval-valued Fuzzy Residual Implicator

把粗糙集理论和区间值模糊集理论结合起来,利用粗糙集理论的构造性方法,提出了一种广义区间值模糊粗糙集理论模型。首先,利用区间值模糊剩余蕴含算子和它的对偶算子,定义了一种广义上下区间值模糊粗糙集近似算子。然后,利用该蕴含算子的性质,讨论了该模型上下近似算子的一系列性质。最后,确立了一些特殊的区间值模糊关系和区间值模糊粗糙集近似算子的联系。

In this paper, we present a general study of general interval-valued fuzzy rough sets integrating the rough set theory with the interval-valued fuzzy set theory by constructive approach. Firstly, by employing the interval-valued fuzzy residual implieator and its dual operator, a generalized upper and lower interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy approximation space are defined. Then some interesting properties of interval-valued fuzzy rough approximation operators are examined based on the properties of interval-valued fuzzy residual implieator on L1. Finally, the connections between special types of interval-valued fuzzy relations and interval-valued fuzzy rough approximation operators are also established.