Abstract
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.
Highlights
Compactness is a property that generalizes the notion of a closed and bounded subset of Euclidean space
Generalizations of compactness have been formulated in many directions, one of them given by using generalized open sets; see, for example, [2]
[8], in 2011, exploited soft sets to introduce the concept of soft topological spaces and study soft separation axioms
Summary
Compactness is a property that generalizes the notion of a closed and bounded subset of Euclidean space. Shabir and Naz [8], in 2011, exploited soft sets to introduce the concept of soft topological spaces and study soft separation axioms. En, researchers started working to generalize topological notions on the soft topological frame In this regard, compactness was one of the topics that received much attention. Is paper is organized as follows: Section 2 gives some main notions of monotonic soft sets and soft topological ordered spaces.
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