On the partial delta differentiability of fuzzy-valued functions via the generalized Hukuhara difference

2021 ◽  
Vol 40 (6) ◽  
Author(s):  
Tri Truong ◽  
Linh Nguyen ◽  
Baruch Schneider
Keyword(s):  
Hukuhara Difference ◽  
Generalized Hukuhara Difference

scholarly journals Generalized Euler-Lagrange Equations for Fuzzy Fractional Variational Problems under gH-Atangana-Baleanu Differentiability

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Jianke Zhang ◽  
Gaofeng Wang ◽  
Xiaobin Zhi ◽  
Chang Zhou
Keyword(s):  
Fractional Derivative ◽  
Lagrange Function ◽  
Variational Problems ◽  
Sufficient Optimality Conditions ◽  
Lagrange Equations ◽  
Hukuhara Difference ◽  
Generalized Hukuhara Difference ◽  
Fractional Variational Problems ◽  
Fractional Calculus Of Variations ◽  
Necessary And Sufficient

We study in this paper the Atangana-Baleanu fractional derivative of fuzzy functions based on the generalized Hukuhara difference. Under the condition of gH-Atangana-Baleanu fractional differentiability, we prove the generalized necessary and sufficient optimality conditions for problems of the fuzzy fractional calculus of variations with a Lagrange function. The new kernel of gH-Atangana-Baleanu fractional derivative has no singularity and no locality, which was not precisely illustrated in the previous definitions.

Newton’s divided gH-difference interpolation formula with unequal spacing for interval-valued function using Hukuhara difference

2021 ◽  
pp. 2250093
Author(s):  
Bapin Mondal ◽  
Md Sadikur Rahman
Keyword(s):  
Significant Role ◽  
Unknown Function ◽  
Interpolation Formula ◽  
Interval Uncertainty ◽  
Hukuhara Difference ◽  
Numerical Examples ◽  
Generalized Hukuhara Difference ◽  
Interval Valued Function ◽  
Definition Of ◽  
Interval Valued

Interval interpolation formulae play a significant role to find the value of an unknown function at some points under interval uncertainty. The objective of this paper is to establish Newton’s divided interpolation formula for interval-valued functions using generalized Hukuhara difference of intervals. For this purpose, arithmetic of intervals, Hukuhara difference and its some properties and concept of interval-valued function have been discussed briefly. Using Hukuhara difference of intervals, the definition of Newton’s divided gH-difference for interval-valued function has been introduced. Then Newton’s divided gH-differences interpolation formula has been derived. Finally, with the help of some numerical examples, the proposed interpolation formula has been illustrated.

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.

A comparison index for interval ordering based on generalized Hukuhara difference

2012 ◽  
Vol 16 (11) ◽  
pp. 1931-1943 ◽  
Author(s):  
Maria Letizia Guerra ◽  
Luciano Stefanini
Keyword(s):  
Hukuhara Difference ◽  
Generalized Hukuhara Difference

scholarly journals Generalized Fuzzy Shapley Function for Fuzzy Games

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Chunqiao Tan ◽  
Xiaohong Chen
Keyword(s):  
Characteristic Function ◽  
Solution Concept ◽  
Axiomatic Characterization ◽  
Hukuhara Difference ◽  
Shapley Function ◽  
Fuzzy Games ◽  
Fuzzy Characteristic

A generalized fuzzy Shapley function for fuzzy games is proposed. First, a game with fuzzy characteristic function is introduced. Based on Hukuhara difference, the fuzzy Hukuhara-Shapley function is proposed as a solution concept to this class of fuzzy games. Some of its properties are shown. An equivalent axiomatic characterization of the fuzzy Hukuhara-Shapley function is given. Furthermore, a generalized fuzzy Shapley function for games with fuzzy coalition and fuzzy characteristic function is developed. It is shown that the simplified expression of the generalized fuzzy Shapley function can be regarded as the generalization of the fuzzy Shapley function defined for some particular games with fuzzy coalition and fuzzy characteristic function.

scholarly journals Some results on the fundamental concepts of fuzzy set theory in intuitionistic fuzzy environment by using α and β cuts

Filomat ◽  
2019 ◽  
Vol 33 (10) ◽  
pp. 3123-3148
Author(s):  
Ömer Akın ◽  
Selami Bayeğ
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Generalized Differentiability ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Generalized Hukuhara Difference ◽  
Strongly Generalized Differentiability ◽  
Characterization Theorems

In this paper we have firstly examined the properties of ? and ? cuts of intuitionistic fuzzy numbers in Rn with the help of well-known Stacking and Characterization theorems in fuzzy set theory. Then, we have studied the generalized Hukuhara difference in intuitionistic fuzzy environment by using the properties of ? and ? cuts and support function. Finally, we have extended the strongly generalized differentiability concept from fuzzy set theory to intuitionistic fuzzy environment and proved the related theorems with this concept.

An optimization technique for national income determination model with stability analysis of differential equation in discrete and continuous process under the uncertain environment

2019 ◽  
Vol 53 (5) ◽  
pp. 1649-1674 ◽  
Author(s):  
Biswajit Sarkar ◽  
Sankar Prasad Mondal ◽  
Sun Hur ◽  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Continuous Process ◽  
Optimization Technique ◽  
National Income ◽  
Significant Implication ◽  
Generalized Hukuhara Derivative ◽  
Fuzzy Environment ◽  
Generalized Hukuhara Difference ◽  
The Stability ◽  
Income Determination

The paper represents a variation of the national income determination model with discrete and continuous process in fuzzy environment, a significant implication in economics planning, by means of fuzzy assumptions. This model is re-recognized and deliberated with fuzzy numbers to estimate its uncertain parameters whose values are not precisely known. Exhibition of imprecise solutions of the concerned model is carried out by using the proposed two methods: generalized Hukuhara difference and generalized Hukuhara derivative (gH-derivative) approaches. Moreover, the stability analysis of the model in two different systems in fuzzy environment is illustrated. Additionally, different illustrative examples for optimization of national income determination model are undertaken with the constructive graph and table for convenience for clarity of the projected approaches.

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