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In this paper, our aim is to consider the new class of log-convex fuzzy-interval-valued function known as log- s -convex fuzzy-interval-valued functions (log- s -convex fuzzy-IVFs). By this concept, we have introduced Hermite–Hadamard inequalities (HH-inequalities) by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation defined on interval space. Moreover, some new Hermite–Hadamard–Fejér inequalities (HH–Fejér-inequalities) and Jensen’s inequalities via log- s -convex fuzzy-IVFs are also established and verified with the support of useful examples. Some special cases are also discussed which can be viewed as applications of fuzzy-interval HH-inequalities. The concepts and approaches of this paper may be the starting point for further research in this area.

New Hermite–Hadamard and Jensen inequalities for log-$$s$$-convex fuzzy-interval-valued functions in the second sense