Abstract
In this work, we prove a Prékopa-Leindler type inequality for the Sugeno integral. More precisely, if 0 < λ 1 and h ((1 - λ)x + λy) ≥ f(x)1-λ g(y)λ, ∀ x, y ∈ ℝn, where h, f and g are nonnegative μ-measurable functions on ℝn, then fℝn hdμ ≥ (f ℝn fdμ) ∧ (fℝn gdμ), for any concave fuzzy measure μ. Also, we derive a general Brunn-Minkowski inequality (standard form) for any homogeneous quasiconcave fuzzy measure μ on ℝn.
| Original language | English |
|---|---|
| Pages (from-to) | 1-11 |
| Number of pages | 11 |
| Journal | International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems |
| Volume | 15 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2007 |
Keywords
- Concave fuzzy measures
- Convex sets
- Sugeno integral
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