TY - JOUR
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 -