TY - JOUR
T1 - The fuzzy integral for monotone functions
AU - Román-Flores, H.
AU - Flores-Franulic, A.
AU - Chalco-Cano, Y.
PY - 2007/2/1
Y1 - 2007/2/1
N2 - In this paper, we give some optimal upper bounds for the Sugeno's integral of monotone functions. More precisely, we show that: If g : [0, ∞) → [0, ∞) is a continuous and strictly monotone function, then the fuzzy integral value p = {cauchy integral}0a g d μ, with respect to the Lebesgue measure μ, verifies the following sharp inequalities:(a) g (a - p) ≥ pfor the increasing case, and(b) g (p) ≥ pfor the decreasing case. Moreover, we show that under adequate conditions, these optimal inequalities provides a powerful tool for solving fuzzy integrals. Also, some examples and application are presented.
AB - In this paper, we give some optimal upper bounds for the Sugeno's integral of monotone functions. More precisely, we show that: If g : [0, ∞) → [0, ∞) is a continuous and strictly monotone function, then the fuzzy integral value p = {cauchy integral}0a g d μ, with respect to the Lebesgue measure μ, verifies the following sharp inequalities:(a) g (a - p) ≥ pfor the increasing case, and(b) g (p) ≥ pfor the decreasing case. Moreover, we show that under adequate conditions, these optimal inequalities provides a powerful tool for solving fuzzy integrals. Also, some examples and application are presented.
KW - Fuzzy measure
KW - Monotone functions
KW - Sugeno's integral
UR - https://www.scopus.com/pages/publications/33846928185
U2 - 10.1016/j.amc.2006.07.066
DO - 10.1016/j.amc.2006.07.066
M3 - Article
AN - SCOPUS:33846928185
SN - 0096-3003
VL - 185
SP - 492
EP - 498
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 1
ER -