Fuzzy Sets and Systems
On the differentiability of set-valued functions defined on a Banach space and mean value theorem
Applied Mathematics and Computation
The Cauchy problem for continuous fuzzy differential equations
Fuzzy Sets and Systems
Fuzzy Sets and Systems - Fuzzy mathematical programming
First order linear fuzzy differential equations under generalized differentiability
Information Sciences: an International Journal
Comparation between some approaches to solve fuzzy differential equations
Fuzzy Sets and Systems
Fuzzy Optimization and Decision Making
A generalization of Hukuhara difference and division for interval and fuzzy arithmetic
Fuzzy Sets and Systems
Generalized derivative and π-derivative for set-valued functions
Information Sciences: an International Journal
Fuzzy functional integro-differential equations under generalized H-differentiability
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Hi-index | 0.20 |
This paper is devoted to studying differential calculus for interval-valued functions by using the generalized Hukuhara differentiability, which is the most general concept of differentiability for interval-valued functions. Conditions, examples and counterexamples for limit, continuity, integrability and differentiability are given. Special emphasis is set to the class F(t)=C.g(t), where C is an interval and g is a real function of a real variable. Here, the emphasis is placed on the fact that F and g do not necessarily share their properties, underlying the extra care that must be taken into account when dealing with interval-valued functions. Two applications of the obtained results are presented. The first one determines a Delta method for interval valued random elements. In the second application a new procedure to obtain solutions to an interval differential equation is introduced. Our results are relevant to fuzzy set theory because the usual fuzzy arithmetic, extension functions and (mathematical) analysis are done on @a-cuts, which are intervals.