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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Analysis on determining the solution of fourth-order fuzzy initial value problem with Laplace operator.
TL;DR: This study presents a new analytical method to extract the fuzzy solution of the fuzzy initial value problem (FIVP) of fourth-order fuzzy ordinary differential equations (FODEs) using the Laplace operator under the strongly generalized Hukuhara differentiability (SGH-differentiability).
Posted Content
Generalized-Hukuhara-Gradient Efficient-Direction Method to Solve Optimization Problems with Interval-valued Functions and its Application in Least Squares Problems
TL;DR: The convergence analysis and the step-wise algorithms of both the methods are presented and it is observed that the W-gH-gradient efficient method converges linearly for a strongly convex interval-valued objective function.
Journal ArticleDOI
Fuzzy Optimal Control Problem of Several Variables
TL;DR: The main results of this paper are illustrated throughout three examples, more specifically, a discussion on the strong solutions (fuzzy solutions) of the authors' problems.
Journal ArticleDOI
Interval linear quadratic regulator and its application for speed control of DC motor in the presence of uncertainties.
TL;DR: In this paper, an analytical investigation of a DC motor with interval uncertainties is performed and a new approach by interval analysis is suggested for optimal control of the system, where the main advantage of using an interval model for uncertainties is that it can be analyzed by only having information about minimum and maximum bounds.
Sobre equações diferenciais para processos fuzzy linearmente correlacionados : aplicações em dinâmica de população
TL;DR: A generalization of the fundamental theorem of calculus is established and an interactive calculus theory is developed for fuzzy processes with local interactivity, that is, locally autocorrelated fuzzy valued 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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