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
Citations
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Two point fuzzy boundary value problem with eigenvalue parameter contained in the boundary condition
TL;DR: In this article, a two point fuzzy boundary value problem is defined under the approach generalized Hukuhara differentiability (gH-differentiability), and the solution method of the fuzzy boundary problem with the basic solutions Φ̂(x, λ ) and χ̂ (x,λ ) which are defined by the special procuder.
Journal ArticleDOI
Solving a fuzzy fractional diffusion model for cancer tumor by using fuzzy transforms
TL;DR: In this article , a fuzzy solution to the mathematical model of a cancer tumor under Caputo-generalized Hukuhara partial differentiability by using fuzzy integral transforms was obtained.
Journal ArticleDOI
On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations
TL;DR: The fuzzy Adomian decomposition method (ADM) and fuzzy modified Laplace decomposition Method (MLDM) are presented to obtain the solutions of fuzzy fractional Navier–Stokes equations in a tube under fuzzy fractionsal derivatives.
Proceedings ArticleDOI
Fuzzy differential equations by fuzzy-transform
Davide Radi,Luciano Stefanini +1 more
TL;DR: The fuzzy transform setting (F-transform), as a tool for general continuous approximation of functions, is proposed to approximate the solution of ordinary, interval or fuzzy (levelwise) differential equations; in particular, one of the basic properties of inverse F-transform allows a good approximation of the solution x(t), starting with the uniform approximation ofThe derivative x'(t) via F- transform.
Journal ArticleDOI
On the stability of solutions of fuzzy differential equations in the quotient space of fuzzy numbers
TL;DR: Some sufficient criteria for the stability, uniformly stability and expo- nentially stability of the trivial solution of the fuzzy differential equations were obtained by using the differential inequalities and the comparison principle for Lyapunov-like functions.
References
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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.
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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.
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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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