Novel Fuzzy Ostrowski Integral Inequalities for Convex Fuzzy-Valued Mappings over a Harmonic Convex Set: Extending Real-Valued Intervals Without the Sugeno Integrals

Mesfer H. Alqahtani, Lou Der-Chyuan (), Fahad Sikander, Yaser Saber () and Cheng-Chi Lee ()
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Mesfer H. Alqahtani: Department of Mathematics, University College of Umluj, University of Tabuk, Tabuk 48322, Saudi Arabia
Lou Der-Chyuan: Department of Computer Science and Information Engineering, Chang Gung University, Taoyuan 33302, Taiwan
Fahad Sikander: Department of Basics Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Jeddah 23442, Saudi Arabia
Yaser Saber: Department of Mathematics, College of Science Al-Zulfi, Majmaah University, P.O. Box 66, Al-Majmaah 11952, Saudi Arabia
Cheng-Chi Lee: Department of Library and Information Science, Fu Jen Catholic University, New Taipei City 24205, Taiwan

Mathematics, 2024, vol. 12, issue 22, 1-29

Abstract: 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.

Keywords: fuzzy Ostrowski inequalities; harmonic convex fuzzy-valued mappings; Kaleva integral; Kulisch–Miranker order relation; fuzzy number space; non-Sugeno integral inequalities; numerical applications of fuzzy inequalities (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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