Generalized differentiability of fuzzy-valued functions
Barnabás Bede,Luciano Stefanini +1 more
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TLDR
Using novel generalizations of the Hukuhara difference for fuzzy sets, new generalized differentiability concepts for fuzzy valued functions are introduced and studied.About:
This article is published in Fuzzy Sets and Systems.The article was published on 2013-11-01 and is currently open access. It has received 497 citations till now. The article focuses on the topics: Fuzzy number & Fuzzy set.read more
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Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability
TL;DR: In this paper, the Atangana-Baleanu fractional derivative of fuzzy functions based on the generalized Hukuhara difference was studied and generalized necessary and sufficient optimality conditions for problems of the fuzzy fractional calculus of variations with a Lagrange function were proved.
Journal ArticleDOI
Non-instantaneous impulses interval-valued fractional differential equations with Caputo-Katugampola fractional derivative concept
Vu Ho,Van Hoa Ngo +1 more
TL;DR: By using the Caputo-Katugampola fractional derivative concept for the interval functions, a non-instantaneous impulsive value problem of interval differential equations is investigated and the Ulam-Hyers-Mittag-Leffler's stability results of the solution are presented.
Journal ArticleDOI
Existence and uniqueness results for fuzzy linear differential-algebraic equations
TL;DR: The existence results for a fuzzy initial value problem of linear differential-algebraic equations and an explicit representation for the solution are discussed and provided.
References
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Journal ArticleDOI
Fuzzy differential equations
TL;DR: F fuzzy-set-valued mappings of a real variable whose values are normal, convex, upper semicontinuous and compactly supported fuzzy sets in Rn are studied and the existence and uniqueness theorem for a solution to a fuzzy differential equation is given.
Journal ArticleDOI
Elementary fuzzy calculus
Roy H. Goetschel,William Voxman +1 more
TL;DR: This paper shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in [4] to define differentiation and integration of fuzzy-valued functions in ways that parallel closely the corresponding definitions for real differentiation and Integration.
Journal ArticleDOI
Differentials of fuzzy functions
Madan L. Puri,Dan A. Ralescu +1 more
TL;DR: The Radstrom embedding theorem is generalized and is used to define the concept of the differential of a fuzzy function.
Journal ArticleDOI
Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations
Barnabás Bede,Sorin G. Gal +1 more
TL;DR: generalized concepts of differentiability (of any order n@?N), which solves this shortcoming of fuzzy number differentiability, are introduced and some concrete applications to partial and ordinary fuzzy differential equations with fuzzy input data of the form c@?g(x).
Journal ArticleDOI
On the fuzzy initial value problem
TL;DR: Generalizations to fuzzy integral equations and fuzzy functional differential equations are indicated and the extension principle and the use of extremal solutions of deterministic initial value problems are applied.
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