The New Versions of Hermite–Hadamard Inequalities for Pre-invex Fuzzy-Interval-Valued Mappings via Fuzzy Riemann Integrals

Abstract

Abstract In this study, we use the fuzzy order relation to show some novel variants of Hermite–Hadamard inequalities for pre-invex fuzzy-interval-valued mappings (F-I∙V-Ms), which we term fuzzy-interval Hermite–Hadamard inequalities and fuzzy-interval Hermite–Hadamard–Fejér inequalities. This fuzzy order relation is defined as the level of the fuzzy-interval space by the Kulisch–Miranker order relation. There are also some new exceptional instances mentioned. The theory proposed in this research is shown with practical examples that demonstrate its usefulness. This paper's approaches and methodologies might serve as a springboard for future study in this field.

Keywords

• Pre-invex fuzzy-interval-valued mappings
• Fuzzy Riemann integral
• Fuzzy-interval Hermite-Hadamard type inequality
• Fuzzy-interval Hermite-Hadamard-Fejér inequality