TY - JOUR
ID - 4552
TI - The Sugeno fuzzy integral of concave functions
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Eshaghi, Madjid
AU - Abbaszadeh, Sadegh
AU - Park, Choonkil
AD - Faculty of Mathematics, Statistics and Computer Sciences, Semnan
University
AD - Department of Computer Science, Paderborn University, Paderborn, Germany
AD - Hanyang University
Y1 - 2019
PY - 2019
VL - 16
IS - 2
SP - 197
EP - 204
KW - Sugeno fuzzy integral
KW - Hermite-Hadamard inequality
KW - Concave function
KW - Supergradient
DO - 10.22111/ijfs.2019.4552
N2 - The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membershipvalue of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is presenthas been well established. Most of the integral inequalities studied in the fuzzy integration context normally considerconditions such as monotonicity or comonotonicity. In this paper, we are trying to extend the fuzzy integrals to theconcept of concavity. It is shown that the Hermite-Hadamard integral inequality for concave functions is not satisfied inthe case of fuzzy integrals. We propose upper and lower bounds on the fuzzy integral of concave functions. We presenta geometric interpretation and some examples in the framework of the Lebesgue measure to illustrate the results.
UR - http://ijfs.usb.ac.ir/article_4552.html
L1 - http://ijfs.usb.ac.ir/article_4552_114f32120dec27a89133d80aa712ff2f.pdf
ER -