Positive or negative solutions to first-order fully fuzzy linear differential equations under generalized differentiability

Chehlabi, M.; Allahviranloo, Tofigh

doi:10.1016/j.asoc.2018.05.040

Cited by 17 publications

(5 citation statements)

References 49 publications

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“…This may be one of the reasons that a large body of studies has been conducted on gH-differentiability of a fuzzy function and FDEs equipped with such a concept, e.g. see [55]- [69]. Concomitantly, in order to address the issue of the existence of gH-derivative of a fuzzy function, the concept of generalized derivative (g-derivative) based on the generalized difference (gdifference) was introduced in 2013 [53].…”

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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“…(18) is called dual fuzzy polynomial. If we use the dual fuzzy polynomial (18) to model a nonlinear function…”

Section: Applying the Solutions Of Fuzzy Equations To Nonlinear Systemsmentioning

confidence: 99%

“…In [17] the compound ( G ′ G )-expansion method is proposed to construct the multiple non-traveling wave solutions of nonlinear PDEs. In [18] positive or negative solutions to first-order fully fuzzy linear differential equations under generalized differentiability are studied. In [19] concreted solutions to fuzzy linear fractional differential equations under Riemann-Liouville H-differentiability is studied.…”

Section: Introductionmentioning

confidence: 99%

Numerical methods for solving fuzzy equations: A survey

Jafari

Razvarz

et al. 2021

Fuzzy Sets and Systems

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“…Zimmerman [3] introduced the first formulation of fuzzy linear programming (FLP) to address the impreciseness of the parameters in linear programming (LP) problems with fuzzy constraints and objective functions. A number of researchers have exhibited their interest to solve the FLP problems [4][5][6][7][8][9][10][11][12][13] and fully FLP problems [14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Predicting the optimal solution in fuzzy linear programming problem

Davoodi¹,

Rahman²

2021

Bul. Kar. Univ. - Math.

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In this paper we try to define a percentage form of LR fuzzy numbers which is a useful form of fuzzy numbers and its’ arithmetics. So, we show how the maximum variation range of optimal value of fuzzy objective function can be predicted by using this form of fuzzy numbers. Since fuzzy problems are generally solved through a complicated manner, the purpose of this study is releasing a kind of prediction for the final solution in the way that the manager can access to an outlook to optimal solution (Z∗) without solving the problem. Finally, optimal value of fuzzy objective function on fuzzy linear programming is predicted when maximum variation range of fuzzy variable have been predetermined.

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Positive or negative solutions to first-order fully fuzzy linear differential equations under generalized differentiability

Cited by 17 publications

References 49 publications

A Review on Fuzzy Differential Equations

A Review on Fuzzy Differential Equations

Numerical methods for solving fuzzy equations: A survey

Predicting the optimal solution in fuzzy linear programming problem

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