Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals
This study presents new fuzzy adaptations of Ostrowski’s integral inequalities through a novel class of convex fuzzy-valued mappings defined over a harmonic convex set, avoiding the use of the Sugeno integral. These innovative inequalities generalize the recently developed interval forms of real-val...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/22/3495 |
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| author | Mesfer H. Alqahtani Der-Chyuan Lou Fahad Sikander Yaser Saber Cheng-Chi Lee |
| author_facet | Mesfer H. Alqahtani Der-Chyuan Lou Fahad Sikander Yaser Saber Cheng-Chi Lee |
| author_sort | Mesfer H. Alqahtani |
| collection | DOAJ |
| description | This study presents new fuzzy adaptations of Ostrowski’s integral inequalities through a novel class of convex fuzzy-valued mappings defined over a harmonic convex set, avoiding the use of the Sugeno integral. These innovative inequalities generalize the recently developed interval forms of real-valued Ostrowski inequalities. Their formulations incorporate integrability concepts for fuzzy-valued mappings (FVMs), applying the Kaleva integral and a Kulisch–Miranker fuzzy order relation. The fuzzy order relation is constructed via a level-wise approach based on the Kulisch–Miranker order within the fuzzy number space. Additionally, numerical examples illustrate the effectiveness and significance of the proposed theoretical model. Various applications are explored using different means, and some complex cases are derived. |
| format | Article |
| id | doaj-art-e85d3c0ddc104095811a5b86831ff326 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-e85d3c0ddc104095811a5b86831ff3262024-11-26T18:11:37ZengMDPI AGMathematics2227-73902024-11-011222349510.3390/math12223495Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno IntegralsMesfer H. Alqahtani0Der-Chyuan Lou1Fahad Sikander2Yaser Saber3Cheng-Chi Lee4Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi ArabiaDepartment of Computer Science and Information Engineering, Chang Gung University, Taoyuan 33302, TaiwanDepartment of Basics Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Jeddah 23442, Saudi ArabiaDepartment of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi ArabiaDepartment of Library and Information Science, Fu Jen Catholic University, New Taipei City 24205, TaiwanThis study presents new fuzzy adaptations of Ostrowski’s integral inequalities through a novel class of convex fuzzy-valued mappings defined over a harmonic convex set, avoiding the use of the Sugeno integral. These innovative inequalities generalize the recently developed interval forms of real-valued Ostrowski inequalities. Their formulations incorporate integrability concepts for fuzzy-valued mappings (FVMs), applying the Kaleva integral and a Kulisch–Miranker fuzzy order relation. The fuzzy order relation is constructed via a level-wise approach based on the Kulisch–Miranker order within the fuzzy number space. Additionally, numerical examples illustrate the effectiveness and significance of the proposed theoretical model. Various applications are explored using different means, and some complex cases are derived.https://www.mdpi.com/2227-7390/12/22/3495fuzzy Ostrowski inequalitiesharmonic convex fuzzy-valued mappingsKaleva integralKulisch–Miranker order relationfuzzy number spacenon-Sugeno integral inequalities |
| spellingShingle | Mesfer H. Alqahtani Der-Chyuan Lou Fahad Sikander Yaser Saber Cheng-Chi Lee Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals Mathematics fuzzy Ostrowski inequalities harmonic convex fuzzy-valued mappings Kaleva integral Kulisch–Miranker order relation fuzzy number space non-Sugeno integral inequalities |
| title | Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals |
| title_full | Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals |
| title_fullStr | Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals |
| title_full_unstemmed | Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals |
| title_short | Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals |
| title_sort | novel fuzzy ostrowski integral inequalities for convex fuzzy valued mappings over a harmonic convex set extending real valued intervals without the sugeno integrals |
| topic | fuzzy Ostrowski inequalities harmonic convex fuzzy-valued mappings Kaleva integral Kulisch–Miranker order relation fuzzy number space non-Sugeno integral inequalities |
| url | https://www.mdpi.com/2227-7390/12/22/3495 |
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