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

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