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 syst...
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| Published in | Journal of mathematics (Hidawi) Vol. 2021; pp. 1 - 12 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cairo
Hindawi
2021
John Wiley & Sons, Inc Wiley |
| Subjects | |
| Online Access | Get full text |
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| 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. |
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| AbstractList | 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. |
| Author | Al-shami, T. M. |
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| Cites_doi | 10.1155/2019/6903809 10.1515/dema-2020-0002 10.30948/afmi.2018.16.3.333 10.2298/fil1813755e 10.1109/GRC.2005.1547365 10.1007/978-94-011-3534-4 10.31559/glm2018.5.3.2 10.1016/s0898-1221(99)00056-5 10.1016/j.camwa.2008.11.009 10.3906/mat-2005-117 10.18576/amis/140617 10.2298/fil1911375a 10.1016/s0898-1221(03)00016-6 10.4169/amer.math.monthly.122.7.619 10.1007/s00500-019-04295-7 10.1007/s00521-011-0722-3 10.1016/j.jksus.2018.06.005 10.1017/s0305004100043668 10.1007/s40314-020-01161-3 10.1080/25765299.2019.1664101 10.1080/16583655.2018.1513701 10.1016/j.camwa.2011.02.006 10.1007/s13370-020-00783-4 10.1007/s00500-009-0465-6 |
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| Copyright | Copyright © 2021 T. M. Al-shami. Copyright © 2021 T. M. Al-shami. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| References | 22 M. E. Abd El-Monsef (2) 1985; 9 25 T. Hida (11) 2014; 8 26 27 29 S. Das (23) 2013; 6 I. Zorlutuna (10) 2012; 3 T. M. Al-Shami (6) 2020; 14 J. L. Kelley (28) 1975 L. Nachbin (3) 1965 T. M. Al-shami (30) 2019; 18 32 33 12 13 14 15 16 17 18 S. Nazmul (24) 2013; 6 19 S. D. Shabir (5) 1991; 22 Z. Pawlak (31) 1991 1 4 7 8 9 20 21 |
| References_xml | – ident: 13 doi: 10.1155/2019/6903809 – volume: 6 start-page: 1 issue: 1 year: 2013 ident: 24 article-title: Neighbourhood properties of soft topological spaces publication-title: Annals of Fuzzy Mathematics and Informatics – volume: 9 start-page: 257 issue: 2 year: 1985 ident: 2 article-title: Some generalized forms of compactness and closedness publication-title: Delta Journal of Science – ident: 20 doi: 10.1515/dema-2020-0002 – ident: 17 doi: 10.30948/afmi.2018.16.3.333 – volume: 8 start-page: 511 issue: 4 year: 2014 ident: 11 article-title: A comparison of two formulations of soft compactness publication-title: Annals of Fuzzy Mathematics and Informatics – ident: 27 doi: 10.2298/fil1813755e – ident: 29 doi: 10.1109/GRC.2005.1547365 – volume-title: Rough Sets: Theoretical Aspects of Reasoning about Data year: 1991 ident: 31 doi: 10.1007/978-94-011-3534-4 – ident: 19 doi: 10.31559/glm2018.5.3.2 – volume-title: General Topology year: 1975 ident: 28 – volume: 6 start-page: 77 issue: 1 year: 2013 ident: 23 article-title: Soft metric publication-title: Annals of Fuzzy Mathematics and Informatics – ident: 7 doi: 10.1016/s0898-1221(99)00056-5 – volume: 22 start-page: 461 year: 1991 ident: 5 article-title: New separation axioms in topological ordered spaces publication-title: Indian Journal of Pure and Applied Mathematics – ident: 25 doi: 10.1016/j.camwa.2008.11.009 – ident: 16 doi: 10.3906/mat-2005-117 – volume: 14 start-page: 1103 issue: 6 year: 2020 ident: 6 article-title: Novel class of ordered separation axioms using limit points publication-title: Applied Mathematics & Information Sciences doi: 10.18576/amis/140617 – ident: 14 doi: 10.2298/fil1911375a – ident: 22 doi: 10.1016/s0898-1221(03)00016-6 – ident: 1 doi: 10.4169/amer.math.monthly.122.7.619 – ident: 32 doi: 10.1007/s00500-019-04295-7 – ident: 9 doi: 10.1007/s00521-011-0722-3 – volume-title: Topology and Order year: 1965 ident: 3 – ident: 18 doi: 10.1016/j.jksus.2018.06.005 – ident: 4 doi: 10.1017/s0305004100043668 – ident: 33 doi: 10.1007/s40314-020-01161-3 – volume: 3 start-page: 171 issue: 2 year: 2012 ident: 10 article-title: Remarks on soft topological spaces publication-title: Annals of Fuzzy Mathematics and Informatics – ident: 21 doi: 10.1080/25765299.2019.1664101 – volume: 18 start-page: 149 issue: 2 year: 2019 ident: 30 article-title: The equivalence between the enriched and extended soft topologie publication-title: Applied and Computational Mathematics – ident: 12 doi: 10.1080/16583655.2018.1513701 – ident: 8 doi: 10.1016/j.camwa.2011.02.006 – ident: 15 doi: 10.1007/s13370-020-00783-4 – ident: 26 doi: 10.1007/s00500-009-0465-6 |
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| Title | Compactness on Soft Topological Ordered Spaces and Its Application on the Information System |
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