不协调区间值决策系统中的α-上、下近似约简

α-lower and upper approximation reductions in inconsistent interval-valued decision systems

研究了不协调区间值决策系统中基于α-容差关系的属性约简问题。针对一种常用的α-容差关系,给出了保持全部决策类的下近似不变的α-下近似约简和保持全部决策类的上近似不变的α-上近似约简的定义,证明了α-上近似约简与已有的α-广义决策约简和α-不确定性保持约简的等价性,以及α-下近似约简与已有的α-确定性保持约简的等价性。讨论了α-上近似约简和α-下近似约简之间的关系,并用例子加以验证。

The focus is on the attribute reductions of inconsistent interval-valued decision systems based on α-tolerance relation. With respect to one kind of α-tolerance relations in inconsistent interval-valued decision systems, notions of α-lower and upper approximate reductions are defined, which keep the lower and upper approximations of all the decision classes unchanged, respectively. Subsequently, the equivalences among the α-upper approximate reduction and α-generalized decision reduction, α-uncertainty maintained reduction, and between α-lower approximate reduction and α-certainty maintained reduction are proved. Meanwhile, the relationships between α-lower approximate reduction and α-upper approximate reduction are discussed in detail, and verified by some examples.