Generalized differentiability of fuzzy-valued functions

Bede, Barnabás; Stefanini, Luciano

doi:10.1016/j.fss.2012.10.003

Cited by 525 publications

(270 citation statements)

References 32 publications

(71 reference statements)

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“…[25,26] Given two fuzzy numbers u, v ∈ E 1 , the generalized Hukuhara difference (gH-difference for short) is the fuzzy number w, if it exists, such that…”

Section: Lemma 26 [23] Let F Gmentioning

confidence: 99%

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Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

Wang¹,

Sun²,

Han³

2017

AAN

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In this paper, we investigate the existence and uniqueness of solution to boundary value problems for a class of nonlinear fuzzy factional differential equations involving the fuzzy gHfractional Caputo derivative. By means of the Schauder fixed point theorem in semi-linear spaces and integral inequality technique, some qualitative results of solutions are obtained. An example is provided from which new results are found.

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“…[25,26] Given two fuzzy numbers u, v ∈ E 1 , the generalized Hukuhara difference (gH-difference for short) is the fuzzy number w, if it exists, such that…”

Section: Lemma 26 [23] Let F Gmentioning

confidence: 99%

“…Definition 2.8. [26] Let t 0 ∈ (a, b) and h be such that t 0 +h ∈ (a, b). Then the generalized Hukuhara derivative of a function F : (a, b) → E 1 at t 0 is defined as…”

Section: Lemma 26 [23] Let F Gmentioning

confidence: 99%

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

Wang¹,

Sun²,

Han³

2017

AAN

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“…Definition 2.2.5: (Bede and Stefanini, 2013). Let , ∈ ℱ(ℝ) , the generalized Hukahara difference (gH-difference) of two fuzzy numbers and is the fuzzy number ∈ ℱ(ℝ), if it exists such that…”

Section: Definition224mentioning

confidence: 99%

“…Each of following conditions guarantees the existence of = ⊖ ∈ ℱ(ℝ) (see 24 for more details) Definition 2.2.6: (Bede and Stefanini, 2013). Let = ⊂ ℝ → ℱ(ℝ) and ∈ be a fixed number, then is called Gh-differentiable at ∈ if: …”

Section: Definition224mentioning

confidence: 99%

Numerical solution of fuzzy initial value problem (FIVP) using optimization

Behroozpoor

Kamyad

Mazarei

2016

Int. j. adv. appl. sci

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In this paper, we introduce a new approach to obtain a novel numerical solution of fuzzy initial value problem (FIVP). This technique is based on optimization problem. In fact, the optimal solution of optimization problem is approximated solution of fuzzy initial value problem. Theoretical consideration is discussed and some examples are presented to show the ability of the method for fuzzy initial value problem.

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“…After the introduction and major innovations in the theory of fuzzy differential equations [4,6,14], the term fuzzy differential equation (FDE) is instantaneously growing as a new area in fuzzy calculus. These equations are acquired interchangeably by incorporating differential equations with fuzzy initial values, fuzzy boundary values or with fuzzy functions as well.…”

Section: Introductionmentioning

confidence: 99%

Adaptive strategies for system of fuzzy differential equation: application of arms race model

Mondal¹,

Khan²,

Razzaq³

et al. 2018

J. Math. Computer Sci.

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The paper presents adaptive stratagems to scrutinize the system of first order fuzzy differential equations (SFDE) in two modes, fuzzy and in crisp sense. Its fuzzy solutions are carried out using two approaches, namely, Zadeh's extension principle and generalized Hukuhara derivative (gH-derivative). While, different defuzzification techniques; central of area method (COA), bisector of area method (BOA), largest of maxima (LOM), smallest of maxima (SOM), mean of maxima (MOM), regular weighted point method (RWPM), graded mean integration value (GMIV), and center of approximated interval (COAI), are employed to discuss the crisp solutions. Moreover, the arms race model (ARM), which have a significant implication in international military planning, are pragmatic examples of system of first order differential equations, but not studied in fuzzy sense, hitherto. Therefore, ARM is re-established and studied here with fuzzy numbers to estimate its uncertain parameters, as a practical utilization of SFDE. Additionally, an illustrative example of ARM is undertaken to clarify the appropriateness of the proposed approaches.

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Generalized differentiability of fuzzy-valued functions

Cited by 525 publications

References 32 publications

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Fuzzy Fractional Differential Equations

Numerical solution of fuzzy initial value problem (FIVP) using optimization

Adaptive strategies for system of fuzzy differential equation: application of arms race model

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