Topological Dynamics of Zadeh’s Extension on Upper Semi-Continuous Fuzzy Sets

Wu, Xinxing; Ding, Xiangling; Lu, Tianxiu; Wang, Jianjun

doi:10.1142/s0218127417501656

Cited by 38 publications

(18 citation statements)

References 38 publications

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“…Energy consumption prediction constitutes an important aspect of energy policies for countries globally, particularly developing countries such as China, where the energy consumption structure is changing at a rapid speed. Numerous models have been introduced for forecasting energy consumption, such as dynamic causality analysis [1], nonlinear and asymmetric analysis [2], time-series analysis [3,4], machine learning models [5], the coupling mathematical model [6,7,8], autoregressive distributed lag model [9], hybrid forecasting system [10,11], machining system [12], fuzzy systems [13], LEAP model [14,15], TIMES model [16,17], NEMS model [18,19] and grey model [20,21,22,23,24,25,26,27,28]. Among these prevalent methods, simple linear regression, multivariate linear regression, and time-series analysis are often significant in accurately demonstrating the phenomena of long-term trends.…”

Section: Introductionmentioning

confidence: 99%

Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption

Wu¹,

Ma²,

Zeng³

et al. 2018

Energy

103

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At present, the energy structure of China is shifting towards cleaner and lower amounts of carbon fuel, driven by environmental needs and technological advances. Nuclear energy, which is one of the major low-carbon resources, plays a key role in China's clean energy development. To formulate appropriate energy policies, it is necessary to conduct reliable forecasts. This paper discusses the nuclear energy consumption of China by means of a novel fractional grey model FAGMO(1,1,k). The fractional accumulated generating matrix is introduced to analyse the fractional grey model properties. Thereafter, the modelling procedures of the FAGMO(1,1,k) are presented in detail, along with the transforms of its optimal parameters. A stochastic testing scheme is provided to validate the accuracy and properties of the optimal parameters of the FAGMO (1,1,k). Finally, this model is used to forecast China's nuclear energy consumption and the results demonstrate that the FAGMO(1,1,k) model provides accurate prediction, outperforming other grey models.

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Section: Introductionmentioning

confidence: 99%

Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption

Wu¹,

Ma²,

Zeng³

et al. 2018

Energy

103

View full text Add to dashboard Cite

show abstract

“…The notion of Li-Yorke sensitivity was firstly introduced by Akin and Kolyada [1] in 2003. More recent results on chaos can be found in [2,3,7,17,18,[20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Shifts, rotations and distributional chaos

Xiang

Liang

2019

Adv Differ Equ

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Let R r 0 , R r 1 : S 1 − → S 1 be rotations on the unit circle S 1 and define f : Σ 2 × S 1 − → Σ 2 × S 1 as f (x, t) = (σ (x), R r x 1 (t)), for x = x 1 x 2 • • • ∈ Σ 2 := {0, 1} N , t ∈ S 1 , where σ : Σ 2 − → Σ 2 is the shift, and r 0 and r 1 are rotational angles. It is first proved that the system (Σ 2 × S 1 , f) exhibits maximal distributional chaos for any r 0 , r 1 ∈ R (no assumption of r 0 , r 1 ∈ R \ Q), generalizing Theorem 1 in Wu and Chen (Topol. Appl. 162:91-99, 2014). It is also obtained that (Σ 2 × S 1 , f) is cofinitely sensitive and (M 1 ,M 1)-sensitive and that (Σ 2 × S 1 , f) is densely chaotic if and only if r 1-r 0 ∈ R \ Q.

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“…Chaotic properties of dynamical systems have been ardently studied since the term chaos (namely, Li-Yorke chaos) was defined in 1975 by Li and Yorke [1]. To describe unpredictability in the evolution of dynamical systems, many properties related to chaos have been discussed (for example, References [2][3][4][5][6][7][8][9][10][11][12][13], where References [4][5][6][7] are some of our works done in recent years). In 1994, Schweizer and Smital in Reference [8] introduced a popular concept named distributional chaos for interval maps, by considering the dynamics of pairs with some statistical properties.…”

Section: Introductionmentioning

confidence: 99%

Distributional Chaoticity of C0-Semigroup on a Frechet Space

Waseem

Tang

2019

Symmetry

Self Cite

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This paper is mainly concerned with distributional chaos and the principal measure of C 0 -semigroups on a Frechet space. New definitions of strong irregular (semi-irregular) vectors are given. It is proved that if C 0 -semigroup T has strong irregular vectors, then T is distributional chaos in a sequence, and the principal measure μ p ( T ) is 1. Moreover, T is distributional chaos equivalent to that operator T t is distributional chaos for every ∀ t > 0 .

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Topological Dynamics of Zadeh’s Extension on Upper Semi-Continuous Fuzzy Sets

Cited by 38 publications

References 38 publications

Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption

Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption

Shifts, rotations and distributional chaos

Distributional Chaoticity of C0-Semigroup on a Frechet Space

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