由反射关系诱导的粗糙集的Kleene和Stone代数
Characterising regular double Stone and pseudocomplemented Kleene algebras in completions of rough sets induced by reflexive relations
AI总结：
研究由反射关系诱导的粗糙集的完成DM(RS)作为空间和完全分配格的条件，推导其作为正则伪补Kleene代数和完全分配双Stone代数的条件，并描述使DM(RS)成为正则双Stone代数的反射关系。
摘要：
我们考虑由反射关系诱导的粗糙集的有序集的完成DM(RS)上的Kleene和Stone代数。我们关注完成形成空间和完全分配格的情况。我们推导出DM(RS)成为正则伪补Kleene代数和完全分配双Stone代数的条件。最后，我们描述了使DM(RS)形成正则双Stone代数的反射关系，这与等价关系的情况相同。我们的结果推广了之前关于由等价关系、准序关系和容差关系诱导的粗糙集代数的研究。
英文摘要：
We consider Kleene and Stone algebras defined on the completion DM(RS) of the ordered set of rough sets induced by a reflexive relation. We focus on the cases where the completion forms a spatial and completely distributive lattice. We derive the conditions under which DM(RS) is a regular pseudocomplemented Kleene algebra and a completely distributive double Stone algebra. Finally, we describe the reflexive relations for which DM(RS) forms a regular double Stone algebra, which is the same structure as in the case of equivalences. Our results generalise earlier findings on algebras of rough sets induced by equivalences, quasiorders, and tolerance relations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
