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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The Karush---Kuhn---Tucker optimality conditions for fuzzy optimization problems
TL;DR: For this class of fuzzy optimization problems, Karush–Kuhn–Tucker type optimality conditions are obtained considering the concept of generalized Hukuhara differentiable and pseudo-invex fuzzy-valued functions.
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On the stability of fuzzy linear dynamical systems
Marzieh Najariyan,Yi Zhao +1 more
TL;DR: Using a theorem proved, it is shown that the stability of fuzzy linear dynamical systems can also be investigated by a matrix called the granular fuzzy Routh–Hurwitz matrix.
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On random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability
TL;DR: In this paper, the solvability of random fuzzy fractional partial integro-differential equations under Caputo generalized Hukuhara differentiability was studied and the existence and uniqueness of two types of integral solutions generated from Darboux problem for nonlinear wave equations were proved using successive approximations method and Gronwall's inequality for stochastic processes.
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q-fractional differential equations with uncertainty
TL;DR: The fuzzy q-derivative and fuzzyq-fractional derivative in Caputo sense is introduced by using generalized Hukuhara difference, and the related theorems and properties are provided in detail and the existence and uniqueness theorem is proved for the solution of FCqF-IVP.
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On Ranking of Continuous Z‐Numbers with Generalized Centroids and Optimization Problems Based on Z‐Numbers
Dong Qiu,Yumei Xing,Rongwen Dong +2 more
TL;DR: A new partial order to rank the Z‐numbers with generalized centroids is defined and the g‐derivative of Z‐number function based on g‐difference is proposed.
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.
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.
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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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