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Abstract In this paper, we introduce the non-convex interval-valued functions for fuzzy-interval-valued functions, which are called "Equation missing"-convex fuzzy-interval-valued functions, by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation given on the interval space. By using the "Equation missing"-convexity concept, we present fuzzy-interval Hermite–Hadamard inequalities for fuzzy-interval-valued functions. Several exceptional cases are debated, which can be viewed as useful applications. Interesting examples that verify the applicability of the theory developed in this study are presented. The results of this paper can be considered as extensions of previously established results.
Khan et al. (2021) studied this question.