It is well known every soft topological space induced from soft information system is soft compact. In this study, we integrate between soft compactness and partially ordered set to introduce new types of soft compactness on the finite spaces and investigate their application on the information system. First, we initiate a notion of monotonic soft sets and establish its main properties. Second, we introduce the concepts of monotonic soft compact and ordered soft compact spaces and show the relationships between them with the help of examples. We give a complete description for each one of them by making use of the finite intersection property. Also, we study some properties associated with some soft ordered spaces and finite product spaces. Furthermore, we investigate the conditions under which these concepts are preserved between the soft topological ordered space and its parametric topological ordered spaces. In the end, we provide an algorithm for expecting the missing values of objects on the information system depending on the concept of ordered soft compact spaces.

中文翻译：

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软拓扑有序空间的紧性及其在信息系统中的应用

众所周知，由软信息系统引起的每个软拓扑空间都是软致密的。在这项研究中，我们在软压缩和部分有序集之间进行集成，以在有限空间上引入新型的软压缩，并研究它们在信息系统中的应用。首先，我们提出单调软集的概念并建立其主要属性。其次，我们介绍了单调软紧空间和有序软紧空间的概念，并借助示例来说明它们之间的关系。通过使用有限交集属性，我们对它们中的每一个给出了完整的描述。此外，我们研究了一些与某些软有序空间和有限乘积空间相关的属性。此外，我们研究了在软拓扑有序空间与其参数化拓扑有序空间之间保留这些概念的条件。最后，我们提供了一种算法，用于根据有序软紧空间的概念来预期信息系统上对象的缺失值。