A novel approach for solving fully fuzzy linear systems and their duality

Abbasi, Seyed Mohammad Mehdi; Jalali, Ahvand

doi:10.3233/jifs-182837

Cited by 7 publications

(2 citation statements)

References 31 publications

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“…In the future, this work can help to determine the flow rate of the traffic on the road by using m-polar fuzzy linear system of equations. Moreover, this work can be used in circuit analysis to balance the flow of current in circuit of the system [47][48][49][50][51].…”

Section: Discussionmentioning

confidence: 99%

LU Decomposition Scheme for Solving m-Polar Fuzzy System of Linear Equations

Koam

Akram

Muhammad

et al. 2020

Mathematical Problems in Engineering

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This paper presents a new scheme for solving m-polar fuzzy system of linear equations (m-PFSLEs) by using LU decomposition method. We assume the coefficient matrix of the system is symmetric positive definite, and we discuss this point in detail with some numerical examples. Furthermore, we investigate the inconsistent m×nm-polar fuzzy matrix equation (m-PFME) and find the least square solution (LSS) of this system by using generalized inverse matrix theory. Moreover, we discuss the strong solution of m-polar fuzzy LSS of the inconsistent m-PFME. In the end, we present a numerical example to illustrate our approach.

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Section: Discussionmentioning

confidence: 99%

LU Decomposition Scheme for Solving m-Polar Fuzzy System of Linear Equations

Koam

Akram

Muhammad

et al. 2020

Mathematical Problems in Engineering

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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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