A note on fuzzy integral inequality of Stolarsky type

A. Flores-Franulič; H. Román-Flores; Y. Chalco-Cano

doi:10.1016/j.amc.2007.05.032

A note on fuzzy integral inequality of Stolarsky type

A. Flores-Franulič
, H. Román-Flores
, Y. Chalco-Cano

Department of Mathematics

Universidad de Tarapacá

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

In this paper, we prove a Stolarsky type inequality for fuzzy integrals. More precisely, we show that:{cauchy integral}₀¹ f fenced(x^{frac(1, a + b)}) d μ ≥ fenced({cauchy integral}₀¹ f fenced(x^{frac(1, a)}) d μ) fenced({cauchy integral}₀¹ f fenced(x^{frac(1, b)}) d μ),where a, b > 0, f : [0, 1] → [0, 1] is a continuous and strictly monotone function and μ is the Lebesgue measure on R.

Original language	English
Pages (from-to)	55-59
Number of pages	5
Journal	Applied Mathematics and Computation
Volume	196
Issue number	1
DOIs	https://doi.org/10.1016/j.amc.2007.05.032
State	Published - 15 Feb 2008

Keywords

Fuzzy measure
Monotone functions
Sugeno integral

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10.1016/j.amc.2007.05.032

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title = "A note on fuzzy integral inequality of Stolarsky type",

abstract = "In this paper, we prove a Stolarsky type inequality for fuzzy integrals. More precisely, we show that:\{cauchy integral\}01 f fenced(xfrac(1, a + b)) d μ ≥ fenced(\{cauchy integral\}01 f fenced(xfrac(1, a)) d μ) fenced(\{cauchy integral\}01 f fenced(xfrac(1, b)) d μ),where a, b > 0, f : [0, 1] → [0, 1] is a continuous and strictly monotone function and μ is the Lebesgue measure on R.",

keywords = "Fuzzy measure, Monotone functions, Sugeno integral",

author = "A. Flores-Franuli{\v c} and H. Rom{\'a}n-Flores and Y. Chalco-Cano",

year = "2008",

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day = "15",

doi = "10.1016/j.amc.2007.05.032",

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T1 - A note on fuzzy integral inequality of Stolarsky type

AU - Flores-Franulič, A.

AU - Román-Flores, H.

AU - Chalco-Cano, Y.

PY - 2008/2/15

Y1 - 2008/2/15

N2 - In this paper, we prove a Stolarsky type inequality for fuzzy integrals. More precisely, we show that:{cauchy integral}01 f fenced(xfrac(1, a + b)) d μ ≥ fenced({cauchy integral}01 f fenced(xfrac(1, a)) d μ) fenced({cauchy integral}01 f fenced(xfrac(1, b)) d μ),where a, b > 0, f : [0, 1] → [0, 1] is a continuous and strictly monotone function and μ is the Lebesgue measure on R.

AB - In this paper, we prove a Stolarsky type inequality for fuzzy integrals. More precisely, we show that:{cauchy integral}01 f fenced(xfrac(1, a + b)) d μ ≥ fenced({cauchy integral}01 f fenced(xfrac(1, a)) d μ) fenced({cauchy integral}01 f fenced(xfrac(1, b)) d μ),where a, b > 0, f : [0, 1] → [0, 1] is a continuous and strictly monotone function and μ is the Lebesgue measure on R.

KW - Fuzzy measure

KW - Monotone functions

KW - Sugeno integral

UR - https://www.scopus.com/pages/publications/38049084700

U2 - 10.1016/j.amc.2007.05.032

DO - 10.1016/j.amc.2007.05.032

M3 - Article

AN - SCOPUS:38049084700

SN - 0096-3003

VL - 196

SP - 55

EP - 59

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 1

ER -

A note on fuzzy integral inequality of Stolarsky type

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Keywords

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