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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Fuzzy Bang-Bang control problem under granular differentiability
TL;DR: This paper proposes a theorem which is proved to be applicable to the FBB control problem and gives complementary theorems to ensure that if the problem has a solution, then the controller assumes its boundary values.
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New approach for studying nonlocal problems related to differential systems and partial differential equations in generalized fuzzy metric spaces
TL;DR: This study considers the solvability of nonlocal problems for fuzzy differential systems under gH-differentiability, and combines the matrix convergent to zero technique with calculations of fuzzy-valued functions in generalized fuzzy metric spaces.
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Existence of solutions to fuzzy differential equations with generalized Hukuhara derivative via contractive-like mapping principles
TL;DR: The existence and uniqueness of solution for fuzzy initial value problems in the setting of a generalized Hukuhara derivative is studied by using some recent results of fixed point of weakly contractive mappings on partially ordered sets.
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Fuzzy Differential Equations for Nonlinear System Modeling With Bernstein Neural Networks
Raheleh Jafari,Wen Yu,Xiaoou Li +2 more
TL;DR: First, fuzzy differential equations are transformed into four ordinary differential equations, then neural models are constructed with the structure of theseordinary differential equations.
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A full fuzzy method for solving differential equation based on Taylor expansion
TL;DR: Using the fuzzy Taylor expansion, the Euler method and its local and global truncation errors are defined for solving fuzzy initial value problems using the concept of generalized Hukuhara differentiability.
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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