Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion
Hypersoft set is a novel area of study which is established as an extension of soft set to handle its limitations. It employs a new approximate mapping called multi-argument approximate function which considers the Cartesian product of attribute-valued disjoint sets as its domain and the power set o...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/6998104 |
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| author | Atiqe Ur Rahman Muhammad Saeed Khuram Ali Khan Rostin Matendo Mabela |
| author_facet | Atiqe Ur Rahman Muhammad Saeed Khuram Ali Khan Rostin Matendo Mabela |
| author_sort | Atiqe Ur Rahman |
| collection | DOAJ |
| description | Hypersoft set is a novel area of study which is established as an extension of soft set to handle its limitations. It employs a new approximate mapping called multi-argument approximate function which considers the Cartesian product of attribute-valued disjoint sets as its domain and the power set of universe as its co-domain. The domain of this function is broader as compared to the domain of soft approximate function. It is capable of handling the scenario where sub-attribute-valued sets are considered more significant than taking merely single set of attributes. In this study, notions of set inclusion, convex (concave) sets, strongly convex (concave) sets, strictly convex (concave) sets, convex hull, and convex cone are conceptualized for the multi-argument approximate function. Based on these characterized notions, some set-theoretic inequalities are established with generalized properties and results. The set-theoretic version of classical Jensen’s type inequalities is also discussed with the help of proposed notions. |
| format | Article |
| id | doaj-art-d15a6c220b14402d9908ed44f6d687e2 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-d15a6c220b14402d9908ed44f6d687e22025-02-03T01:11:57ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/6998104Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set InclusionAtiqe Ur Rahman0Muhammad Saeed1Khuram Ali Khan2Rostin Matendo Mabela3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Maths and Computer ScienceHypersoft set is a novel area of study which is established as an extension of soft set to handle its limitations. It employs a new approximate mapping called multi-argument approximate function which considers the Cartesian product of attribute-valued disjoint sets as its domain and the power set of universe as its co-domain. The domain of this function is broader as compared to the domain of soft approximate function. It is capable of handling the scenario where sub-attribute-valued sets are considered more significant than taking merely single set of attributes. In this study, notions of set inclusion, convex (concave) sets, strongly convex (concave) sets, strictly convex (concave) sets, convex hull, and convex cone are conceptualized for the multi-argument approximate function. Based on these characterized notions, some set-theoretic inequalities are established with generalized properties and results. The set-theoretic version of classical Jensen’s type inequalities is also discussed with the help of proposed notions.http://dx.doi.org/10.1155/2022/6998104 |
| spellingShingle | Atiqe Ur Rahman Muhammad Saeed Khuram Ali Khan Rostin Matendo Mabela Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion Journal of Function Spaces |
| title | Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion |
| title_full | Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion |
| title_fullStr | Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion |
| title_full_unstemmed | Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion |
| title_short | Set-Theoretic Inequalities Based on Convex Multi-Argument Approximate Functions via Set Inclusion |
| title_sort | set theoretic inequalities based on convex multi argument approximate functions via set inclusion |
| url | http://dx.doi.org/10.1155/2022/6998104 |
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