TY - JOUR
T1 - Sugeno integral and geometric inequalities
AU - Roman-Flores, Heriberto
AU - Chalco-Cano, Yurilev
PY - 2007/2
Y1 - 2007/2
N2 - 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.
AB - 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.
KW - Concave fuzzy measures
KW - Convex sets
KW - Sugeno integral
UR - https://www.scopus.com/pages/publications/33847375086
U2 - 10.1142/S0218488507004340
DO - 10.1142/S0218488507004340
M3 - Article
AN - SCOPUS:33847375086
SN - 0218-4885
VL - 15
SP - 1
EP - 11
JO - International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems
JF - International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems
IS - 1
ER -