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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Journal ArticleDOI
Stability for initial value problems of fuzzy Volterra integro-differential equation with fractional order derivative
Ho Vu,Ngo Van Hoa,Truong Vinh An +2 more
Journal ArticleDOI
A Single Layer Functional Link Artificial Neural Network based on Chebyshev Polynomials for Neural Evaluations of Nonlinear Nth Order Fuzzy Differential Equations
TL;DR: Nonlinear nth order FDEs are approximated, heuristically, on using Chebyshev neural network, which is a type of single layer functional link artificial neural network (FLANN) and explication of generalized Hukuhara differentiability (gH-differentiability) is added for the n fourth order differentiability of fuzzy-valued functions.
Journal ArticleDOI
Fuzzy reproducing kernel space method for solving fuzzy boundary value problems
TL;DR: This work uses the fuzzy reproducing kernel method to solve the second-order fuzzy boundary value problem and describes the fuzzy inner product space and the fuzzy Hilbert space.
Journal ArticleDOI
A unified generalization for Hukuhara types differences and derivatives: Solid analysis and comparisons
TL;DR: In this paper , a class of scalar multiplication and differences is proposed, and a necessary and sufficient condition of the existence of the introduced differences is obtained, and the existing result for the derivative is studied.
Book ChapterDOI
A Davidon-Fletcher-Powell Type Quasi-Newton Method to Solve Fuzzy Optimization Problems
TL;DR: A Davidon-Fletcher-Powell type quasi-Newton method is proposed to capture nondominated solutions of fuzzy optimization problems, which finds that the sequence in the proposed method has superlinear convergence rate.
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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