Research Article Compactness on Soft Topological Ordered Spaces and Its Application on the Information System T. M. Al-shami Department of Mathematics, Sana’a University, Sana’a, Yemen CorrespondenceshouldbeaddressedtoT.M.Al-shami;tareqalshami83@gmail.com Received 28 October 2020; Accepted 17 December 2020; Published 18 January 2021 AcademicEditor:Ching-FengWen Copyright©2021T.M.Al-shami.isisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. It is well known every soft topological space induced from soft information system is soft compact. In this study, we integrate betweensoftcompactnessandpartiallyorderedsettointroducenewtypesofsoftcompactnessonthefinitespacesandinvestigate 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,weinvestigatetheconditionsunderwhichtheseconceptsarepreservedbetweenthesofttopologicalorderedspace anditsparametrictopologicalorderedspaces.Intheend,weprovideanalgorithmforexpectingthemissingvaluesofobjectson the information system depending on the concept of ordered soft compact spaces. 1. Introduction Compactness is a property that generalizes the notion of a closed and bounded subset of Euclidean space. It has been describedbyusingthefiniteintersectionpropertyforclosed sets. e important motivations beyond studying com- pactnesshavebeengivenin[1].Withoutdoubt,theconcept of compactness occupied a wide area of topologists’ atten- tion. Many relevant ideas to this concept have been intro- duced and studied. Generalizations of compactness have been formulated in many directions, one of them given by using generalized open sets; see, for example, [2]. In 1965, Nachbin [3] combined a partial order relation with a topological space to define a new mathematical structure, namely, a topological ordered space. en, McCartan [4] formulated ordered separation axioms with respect to open sets and neighbourhoods which were de- scribed by increasing or decreasing operators. Shabir and Gupta [5] extended these ordered separation axioms in the cases of T 1 -ordered and T 2 -ordered spaces using semiopen sets.Recently,Al-ShamiandAbo-Elhamayel[6]introduced new types of ordered separation axioms. In1999,Molotdsov[7]cameupwiththeideaofsoftsets fordealingwithuncertaintiesandvagueness.ShabirandNaz [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 at- tention. It was presented and explored firstly by Molodtsov Ayg .. uno˘ glu and Ayg .. un, and Zorlutuna et al. [9, 10]. en, Hida[11]comparedbetweentwotypesofsoftcompactness. Afterthat,Al-Shamietal.[12]definedalmostsoftcompact and mildly soft compact spaces and investigated the main properties. Lack of consideration in the privacy of soft sets by some authors causes emerging some alleged results, es- pecially those related to the properties of soft compactness. erefore,theauthorsof[13–17]carriedoutsomecorrective studies in this regard. In2019,Al-Shamietal.[18]definedtopologicalordered spacesonsoftsetting.eystudiedmonotonicsoftsetsand thenutilizedthemtopresent p-soft T i -orderedspaces.Also, they [19] presented soft I(D, B)-continuous mappings and establishedseveralgeneralizationsofthemusinggeneralized Hindawi Journal of Mathematics Volume 2021, Article ID 6699092, 12 pages https://doi.org/10.1155/2021/6699092