TY - JOUR
T1 - Algebra of generalized Hukuhara differentiable interval-valued functions
T2 - review and new properties
AU - Chalco-Cano, Y.
AU - Maqui-Huamán, Gino G.
AU - Silva, G. N.
AU - Jiménez-Gamero, M. D.
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/11/15
Y1 - 2019/11/15
N2 - This article deals with the algebra of gH-differentiable interval-valued functions. Specifically, we give conditions for the gH-differentiability of the sum and the gH-difference of two gH-differentiable interval-valued functions; we also consider the product and the composition of a differentiable real function and a gH-differentiable interval-valued function. We briefly review existing results on the topic and show that some of them are not correct. New properties are also presented. Therefore, this article corrects, complements and generalizes previously obtained results. Some examples and counterexamples illustrate the theory.
AB - This article deals with the algebra of gH-differentiable interval-valued functions. Specifically, we give conditions for the gH-differentiability of the sum and the gH-difference of two gH-differentiable interval-valued functions; we also consider the product and the composition of a differentiable real function and a gH-differentiable interval-valued function. We briefly review existing results on the topic and show that some of them are not correct. New properties are also presented. Therefore, this article corrects, complements and generalizes previously obtained results. Some examples and counterexamples illustrate the theory.
KW - Algebra of interval-valued functions
KW - Fuzzy-valued functions
KW - Generalized Hukuhara differentiability
KW - Interval-valued functions
UR - https://www.scopus.com/pages/publications/85064714935
U2 - 10.1016/j.fss.2019.04.006
DO - 10.1016/j.fss.2019.04.006
M3 - Article
AN - SCOPUS:85064714935
SN - 0165-0114
VL - 375
SP - 53
EP - 69
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
ER -