Sugeno Integral Inequalities for Convex Functions: New Sandor-Type Bounds and Their Ramifications
DOI:
https://doi.org/10.31185/bsj.Vol23.Iss44.1717Keywords:
Sugeno integral • fuzzy measure • convex function • Sandor-type inequality • Hermite–Hadamard inequality • s-convexity • level-set method • monotone measure.Abstract
Motivated by recent developments and the growing demand for precise integral bounds in aggregation models, this work investigates the extension of classical convexity inequalities to non-additive measures. We establish new lower and upper bounds for the Sugeno integral of convex, s-convex, and quasi-convex functions defined on compact real intervals. These bounds constitute genuine analogues, within the non-additive setting, of the refinement established by Sandor in 1997 for the classical Riemann integral. The proofs rely on level-set analysis, which proves particularly effective in capturing the minimum–maximum structure of the Sugeno integral; none of the results invoke the classical monotone-convergence arguments. Beyond the theoretical development, we provide a series of worked numerical examples and a compact comparison table, enabling the reader to assess the relative size of the bounding regions for several representative families of functions. We further discuss the connections between our results and both the Hermite–Hadamard inequality and the Choquet integral, and we conclude by posing several problems that merit future investigation.
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