Rough set theory over two universes is a generalization of rough set model to find accurate approximations for uncertain concepts in information systems in which uncertainty arises from existence of interrelations between the three basic sets: objects, attributes, and decisions. In this work, multisets are approximated in a crisp two-universe approximation space using binary ordinary relation and multi relation. The concept of two universe approximation is applied for defining lower and upper approximations of multisets. Properties of these approximations are investigated, and the deviations between them and corresponding notions are obtained; some counter examples are given. The suggested notions can help in the modification of the decision-making for events in which objects have repetitions such as patients visiting a doctor more than one time; an example for this case is given.

中文翻译：

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双宇宙逼近空间中的多集概念

两个宇宙的粗糙集理论是粗糙集模型的推广，用于在信息系统中找到不确定概念的准确近似值，其中不确定性源于三个基本集合之间的相互关系：对象、属性和决策。在这项工作中，使用二元普通关系和多重关系在一个清晰的双宇宙近似空间中近似多重集。两个宇宙近似的概念用于定义多重集的下近似和上近似。研究了这些近似的性质，并获得了它们与相应概念之间的偏差；给出了一些反例。建议的概念可以帮助修改对象具有重复的事件的决策制定，例如患者就诊一次以上；