Sugeno integral and geometric inequalities

Heriberto Roman-Flores; Yurilev Chalco-Cano

doi:10.1142/S0218488507004340

Sugeno integral and geometric inequalities

Heriberto Roman-Flores
, Yurilev Chalco-Cano

Departamento de Matemática

Universidad de Tarapacá

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

52 Citas (Scopus)

Resumen

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 f_ℝn hdμ ≥ (f _ℝn fdμ) ∧ (f_ℝn 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.

Idioma original	Inglés
Páginas (desde-hasta)	1-11
Número de páginas	11
Publicación	International Journal of Uncertainty, Fuzziness and Knowldege-Based Systems
Volumen	15
N.º	1
DOI	https://doi.org/10.1142/S0218488507004340
Estado	Publicada - feb 2007

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title = "Sugeno integral and geometric inequalities",

abstract = "In this work, we prove a Pr{\'e}kopa-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.",

keywords = "Concave fuzzy measures, Convex sets, Sugeno integral",

author = "Heriberto Roman-Flores and Yurilev Chalco-Cano",

year = "2007",

month = feb,

doi = "10.1142/S0218488507004340",

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T1 - Sugeno integral and geometric inequalities

AU - Roman-Flores, Heriberto

AU - Chalco-Cano, Yurilev

PY - 2007/2

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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

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DO - 10.1142/S0218488507004340

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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 -

Sugeno integral and geometric inequalities

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