Calculus for interval-valued functions using generalized Hukuhara derivative and applications

2013 ◽  
Vol 219 ◽  
pp. 49-67 ◽  
Author(s):  
Y. Chalco-Cano ◽  
A. Rufián-Lizana ◽  
H. Román-Flores ◽  
M.D. Jiménez-Gamero
Keyword(s):  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Interval Valued

A novel difference and derivative of linearly correlated fuzzy number-valued functions

2022 ◽  
pp. 1-17
Author(s):  
Yonghong Shen
Keyword(s):  
Fuzzy Number ◽  
Fuzzy Numbers ◽  
Hukuhara Difference ◽  
Interval Numbers ◽  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Generalized Hukuhara Difference ◽  
Interval Valued

In the present paper, the notion of the linearly correlated difference for linearly correlated fuzzy numbers is introduced. Especially, the linearly correlated difference and the generalized Hukuhara difference are coincident for interval numbers or even symmetric fuzzy numbers. Accordingly, an appropriate metric is induced by using the norm and the linearly correlated difference in the set of linearly correlated fuzzy numbers. Based on the symmetry of the basic fuzzy number, the linearly correlated derivative is proposed by the linearly correlated difference of linearly correlated fuzzy number-valued functions. In both non-symmetric and symmetric cases, the equivalent characterizations of the linearly correlated differentiability of a linearly correlated fuzzy number-valued function are established, respectively. Moreover, it is shown that the linearly correlated derivative is consistent with the generalized Hukuhara derivative for interval-valued functions.

scholarly journals A New Method to Find Fuzzy Nth Order Derivation and Applications to Fuzzy Nth Order Arithmetic Based on Generalized H-Derivation

2014 ◽  
Vol 4 (2) ◽  
pp. 105-121
Author(s):  
Laleh Hooshangian ◽  
Tofigh Allahviranloo
Keyword(s):  
Differential Equations ◽  
New Method ◽  
Order Derivative ◽  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Order Arithmetic ◽  
Order Derivation

In this paper, fuzzy nth-order derivative for n in N is introduced. To do this, nth-order derivation under generalized Hukuhara derivative here in discussed. Calculations on the fuzzy nth-order derivative on fuzzy functions and their relationships, in general, are introduced. Then, the fuzzy nth-order differential equations is solved, for n in N.

scholarly journals Application of Contractive-like Mapping Principles to Fuzzy Functional Differential Equation

2018 ◽  
Vol 20 ◽  
pp. 02008
Author(s):  
Vu Ho
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solution ◽  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative ◽  
Functional Differential

In this paper, we prove the existence and uniqueness of solution for the fuzzy functional differential equation under generalized Hukuhara derivative via contractive-like mapping principles.

scholarly journals Existence Theorems for Solutions to Set-Valued Stochastic Differential Equations and Applications

2012 ◽  
Vol 1 ◽  
pp. 1-15
Author(s):  
Vu Ho ◽  
Van Hoa Ngo
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Wiener Process ◽  
Langevin Equation ◽  
Stock Prices ◽  
Hausdorff Space ◽  
Existence Theorems ◽  
Uniqueness Of Solution ◽  
Hukuhara Derivative ◽  
Interval Valued

In this paper, a class of new stochastic differential equations on semilinear Hausdorff space under Hukuhara derivative, called set-valued stochastic differential equations (SSDEs) driven by a Wiener process. Moreover, some corresponding properties of SSDEs are discussed such as existence, uniqueness of solution. Finaly, we give some applications to models of interval-valued stochastic differential equations such as stock prices model and the Langevin equation.

scholarly journals GENERAL SOLUTION OF BASSET EQUATION WITH CAPUTO GENERALIZED HUKUHARA DERIVATIVE

2016 ◽  
Vol 6 (1) ◽  
pp. 119-130
Author(s):  
A. Armand ◽  
◽  
T. Allahviranloo ◽  
Z. Gouyandeh
Keyword(s):  
General Solution ◽  
Hukuhara Derivative ◽  
Generalized Hukuhara Derivative
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