Compactness on Soft Topological Ordered Spaces and Its Application on the Information System

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.

Automated summary

This study introduces new concepts of soft compactness by combining soft information systems and partially ordered sets, focusing on their applications in finite spaces. The research explores notions of monotonic soft sets, monotonic soft compactness, and ordered soft compact spaces, showing their interrelationships through examples. Complete descriptions are provided for each concept using the finite intersection property.