%0 Journal Article %T Study on differentiability problems of interval-valued functions %A Bao, Yu-E %A Li , Jin-Jun %A Bai, Eer-Dun %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 11 %@ ISSN 2008-1901 %F Bao2017 %X In this paper, we give the concepts of \(H\)-directional differentiability and \(D\)-directional differentiability of interval-valued functions. Then we discuss the properties of \(H\)-directional differentiable interval-valued functions and \(D\)-directional differentiable interval-valued functions. The necessary and sufficient conditions for the \(H\)-directional differentiability are given together with the sufficient conditions and the necessary and sufficient conditions for \(D\)-directional differentiability of interval-valued functions. Then we discuss the relationship between the two directional differentiability and prove these directional differentiability can be equivalent under a certain conditions. %9 journal article %R 10.22436/jnsa.010.11.06 %U http://dx.doi.org/10.22436/jnsa.010.11.06 %P 5677--5689 %0 Journal Article %T Generalized derivative and \(\pi\)-derivative for set-valued functions %A Y. Chalco-Cano %A H. Román-Flores %A M. D. Jiménez-Gamero %J Inform. Sci. %D 2011 %V 181 %F Chalco-Cano2011 %0 Journal Article %T Calculus for interval-valued functions using generalized Hukuhara derivative and applications %A Y. Chalco-Cano %A A. Rufián-Lizan %A H. Román-Flores %A M. D. Jiménez-Gamero %J Fuzzy Sets and Systems %D 2013 %V 219 %F Chalco-Cano2013 %0 Journal Article %T Fractional calculus for interval-valued functions %A V. Lupulescu %J Fuzzy Sets and Systems %D 2015 %V 265 %F Lupulescu 2015 %0 Book %T Interval Analysis %A R. E. Moore %D 1966 %I Prentice-Hall %C New Jersey %F Moore 1966 %0 Journal Article %T Optimality conditions for generalized differentiable interval-valued functions %A R. Osuna-Gómez %A Y. Chalco-Cano %A B. Hernández-Jiménez %A G. Ruiz-Garzón %J Inform. Sci. %D 2015 %V 321 %F Osuna-Gómez2015 %0 Journal Article %T Generalized Hukuhara differentiability of interval-valued functions and interval differential equations %A L. Stefanini %A B. Bede %J Nonlinear Anal. %D 2009 %V 71 %F Stefanini2009 %0 Journal Article %T The Karush-Kuhn-Tucker optimality conditions in an optimization problem with interval-valued objective functions %A H.-C. Wu %J European J. Oper. Res. %D 2007 %V 176 %F Wu2007 %0 Journal Article %T The Karush-Kuhn-Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions %A H.-C. Wu %J European J. Oper. Res. %D 2009 %V 196 %F Wu 2009