Fuzzy Bang-Bang control problem under granular differentiability

Mazandarani, Mehran; Zhao, Yi

doi:10.1016/j.jfranklin.2018.05.022

Cited by 46 publications

(9 citation statements)

References 26 publications

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“…The main reason why grderivative has been proposed is to overcome drawbacks of the approaches -namely H-derivative, SGH-derivative, gHderivative, g-derivative, and π-derivative -that employ fuzzy standard interval arithmetic (FSIA) to handle FDEs. The drawbacks would be outlined as: the existence of the derivative, monotonic uncertainty, multiplicity of solutions, doubling property, symmetric uncertainty around zero problem (SUAZ problem) and unnatural behavior in modeling (UBM) phenomenon, for more details see [74], [92]- [97]. Some of the drawbacks will be explained briefly in Section V. Further research work inspired by the concept of gr-derivative can be found in [98]- [111].…”

Section: A Integer Order Fuzzy Differential Equationsmentioning

confidence: 99%

A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

2021

IEEE Access

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Since the term "Fuzzy differential equations" (FDEs) emerged in the literature in 1978, prevailing research effort has been dedicated not only to the development of the concepts concerning the topic, but also to its potential applications. This paper presents a chronological survey on fuzzy differential equations of integer and fractional orders. Attention is concentrated on the FDEs in which a definition of fuzzy derivative of a fuzzy number-valued function has been taken into account. The chronological rationale behind considering FDEs under each concept of fuzzy derivative is highlighted. The pros and cons of each approach dealing with FDEs are also discussed. Moreover, some of the proposed FDEs applications and methods for solving them are investigated. Finally, some of the future perspectives and challenges of fuzzy differential equations are discussed based on our personal view point.

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Section: A Integer Order Fuzzy Differential Equationsmentioning

confidence: 99%

A Review on Fuzzy Differential Equations

Mazandarani¹,

Li²

2021

IEEE Access

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“…Here, for defuzzifying the Hamiltonian function we use the gr-differentiability approach (inspired by Mazandarani and Zhao 2018; as follows…”

Section: Optimal Control Policymentioning

confidence: 99%

Control the preservation cost of a fuzzy production inventory model of assortment items by using the granular differentiability approach

Khatua

Kar

2020

Comp. Appl. Math.

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This paper deals with a single period fuzzy production inventory model with the assortment items in a finite time horizon. Here, we tried to implement the preservation technology for decreasing the deterioration rate and control the preservation cost of the deteriorated products. In harmony with the real-life uncertain production inventory system, the decision variables and some of the parameters of the proposed model are assumed to be fuzzy variables. So a fuzzy dynamical system has been developed and solved for controlling the system. The optimality of the objective function in fuzzy optimal control has been derived and we have introduced a new approach, the granular differentiability for defuzzifying the system. Then the defuzzified optimal control problem is solved by using Pontryagin's maximum principle. Here, we have used the Runge-Kutta forward-backward method of fourth-order through MATLAB software. The proposed model is illustrated through a numerical example to determine the optimality conditions and the results are shown both in tabular form and graphically.

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“…In this section, we recall some essential facts from basic concepts of fuzzy analysis used throughout this paper; see (Bede 2013;Bede and Stefanini 2013;Lakshmikantham and Mohapatra 2003;Mazandarani and Zhao 2018;Stefanini and Bede 2009). Let E be the space of all fuzzy numbers on R having the parametric form…”

Section: Preliminariesmentioning

confidence: 99%

Fuzzy delay differential equations under granular differentiability with applications

Son¹,

Long

Dong

2019

Comp. Appl. Math.

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In this paper, we consider a new setting of fuzzy delay differential equations by employing the concepts of granular differentiability. Firstly, we establish some basic properties of complete granular metric space. Then we study the local and global existence and uniqueness of integral fuzzy solution. For the first task, we use successive approximation technique combined with Gronwall's lemma. The second task will be solved by Banach contraction principle in weighted metric space defined by granular distance. Additionally, we demonstrate the theoretical results by solving some real-world models in both analytical method and numerical method. The first model is often referred to the exponential growth, namely time-delay growth Malthusian model. The second model is one type of dynamical systems, which is used for studies involving large amounts of tissues, called Ehrlich ascites tumor model with delay. Furthermore, we introduce the Mackey-Glass model which is considered as a useful tool for times series prediction in the neutral network and fuzzy logic fields. Finally, we represent the surface of fuzzy solution for visible identification mark-on. Keywords Granular differentiability • Fuzzy delay differential equations • Malthusian growth model • Ehrlich ascites tumor model • Mackey-Glass time series model Mathematics Subject Classification 34A07 • 35R13 Communicated by Anibal Tavares de Azevedo.

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Fuzzy Bang-Bang control problem under granular differentiability

Cited by 46 publications

References 26 publications

A Review on Fuzzy Differential Equations

A Review on Fuzzy Differential Equations

Control the preservation cost of a fuzzy production inventory model of assortment items by using the granular differentiability approach

Fuzzy delay differential equations under granular differentiability with applications

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