广义拟阵的约简与近似算子

Reduction and Approximation Operators of Greedoid

广义拟阵作为拟阵结构的拓广形式之一,在许多领域扮演着重要的角色。为了将广义拟阵理论进一步地拓广,首先基于覆盖粗糙集,提出可约广义拟阵的定义,并给出相关的算法和实例。其次,为了实现不同广义拟阵知识层面上知识的表述,将拟阵中秩强映射的定义推广到广义拟阵中,并且基于此定义,对于广义拟阵提出一种特殊的秩强映射——保基秩强映射。然后,基于粗糙集近似算子的定义,给出广义拟阵相应的近似算子及其相关性质的证明,以此实现在同一个广义拟阵知识层面上知识的表述。最后将广义拟阵中的保基秩强映射与近似算子相结合,提出在保基秩强映射下广义拟阵间近似算子的关系。

Greedoid, as one of generalized structures of a matroid, plays an important role in many fields. In order to extend the greedoid theory further, firstly, based on covering rough set, the definition of reducible greedoid is proposed, and the related algorithm and examples are given. Secondly, in order to express knowledge on different knowledge levels of greedoids, the definition of rank strong map is extended from matroid to greedoid. Based on the new definition, a special rank strong map is proposed for greedoids, which is called base-preserving rank strong map. Afterwards, based on the definition of approximation operators of rough set, the definitions of some pairs of approximation operators of greeoid is given, and some related properties are discussed, so as to realize the representation of knowledge on the same knowledge level of greedoid. Finally, the relationships of approximation operators between greeoids under the base-preserving rank strong map are proposed by combining the base-preserving rank strong map with approximation operators.