Mathematical Modeling of Possibility Markov Chains by Possibility Theory

Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.

Modelling Land Use/Land Cover Change of River Rwizi Catchment, South-Western Uganda Using GIS and Markov Chain Model

Analysis of catchment Land use/Land cover (LULC) change is a vital tool in ensuring sustainable catchment management. The study analyzed land use/land cover changes in the Rwizi catchment, south western Uganda from 1989-2019 and projected the trend by 2040. Landsat images, field observations, key informant interviews and focus group discussions were used to collect data. Changes in cropland, forestland, built up area, grazing land, wetland and open water bodies were analyzed in ArcGIS version 10.2.2 and ERDAS IMAGINE 14 software and a Markov chain model. All the LULC classes increased in area except grazing land. Forest land and builtup area between 2009-2019 increased by 370.03% and 229.53% respectively. Projections revealed an increase in forest land and builtup area by 2030 and only built up area by 2040. LULCC in the catchment results from population pressure, reduced soil fertility and high value of agricultural products.

Forecast future disasters using hydro-meteorological datasets in the Yamuna river basin,Western Himalaya:Using Markov Chain and LSTM approaches

This research aim to evaluate hydro-meteorological data from the Yamuna River Basin,Uttarakhand,India,utilizing Extreme Value Distribution of Frequency Analysis and the Markov Chain Approach.This method assesses persistence and allows for combinatorial probability estimations such as initial and transitional probabilities.The hydrologic data was generated(in-situ)and received from Uttarakhand Jal Vidut Nigam Limited(UJVNL),and meteorological data was acquired from NASA’s archives MERRA-2 product.A total of sixteen years(2005-2020)of data was used to foresee daily Precipitation from 2020 to 2022.MERRA-2 products are utilized as observed and forecast values for daily Precipitation throughout the monsoon season,which runs from July to September.Markov Chain and Long Short-Term Memory(LSTM)findings for 2020,2021,and 2022 were observed,and anticipated values for daily rainfall during the monsoon season between July and September.According to test findings,the artificial intelligence technique cannot anticipate future regional meteorological formations;the correlation coefficient R^(2) is around 0.12.According to the randomly verified precipitation data findings,the Markov Chain model has a success rate of 79.17 percent.The results suggest that extended return periods should be a warning sign for drought and flood risk in the Himalayan region.This study gives a better knowledge of the water budget,climate change variability,and impact of global warming,ultimately leading to improved water resource management and better emergency planning to the establishment of the Early Warning System(EWS)for extreme occurrences such as cloudbursts,flash floods,landslides hazards in the complex Himalayan region.

Aligned Ion Conduction Pathway of Polyrotaxane‑Based Electrolyte with Dispersed Hydrophobic Chains for Solid‑State Lithium–Oxygen Batteries

A critical challenge hindering the practical application of lithium–oxygen batteries(LOBs)is the inevitable problems associated with liquid electrolytes,such as evaporation and safety problems.Our study addresses these problems by proposing a modified polyrotaxane(mPR)-based solid polymer electrolyte(SPE)design that simultaneously mitigates solvent-related problems and improves conductivity.mPR-SPE exhibits high ion conductivity(2.8×10^(−3)S cm^(−1)at 25℃)through aligned ion conduction pathways and provides electrode protection ability through hydrophobic chain dispersion.Integrating this mPR-SPE into solid-state LOBs resulted in stable potentials over 300 cycles.In situ Raman spectroscopy reveals the presence of an LiO_(2)intermediate alongside Li_(2)O_(2)during oxygen reactions.Ex situ X-ray diffraction confirm the ability of the SPE to hinder the permeation of oxygen and moisture,as demonstrated by the air permeability tests.The present study suggests that maintaining a low residual solvent while achieving high ionic conductivity is crucial for restricting the sub-reactions of solid-state LOBs.

WIN-WIN CHAINS

The philosophical concept of one bond connecting the world is an established scientific and economic phenomenon today.The global industrial and supply chains are symbols of that universal link of fraternity,cooperation and globalization.Despite a few major economies still trying to push forward a decoupling agenda and favoring a“small yard,high fence”strategy,globalization and cooperation remain a global trend.

Bearing Fault Diagnosis Based on the Markov Transition Field and SE-IShufflenetV2 Model

A bearing fault diagnosis method based on the Markov transitionfield(MTF)and SEnet(SE)-IShufflenetV2 model is proposed in this paper due to the problems of complex working conditions,low fault diagnosis accuracy,and poor generalization of rolling bearing.Firstly,MTF is used to encode one-dimensional time series vibration sig-nals and convert them into time-dependent and unique two-dimensional feature images.Then,the generated two-dimensional dataset is fed into the SE-IShufflenetV2 model for training to achieve fault feature extraction and classification.This paper selects the bearing fault datasets from Case Western Reserve University and Paderborn University to experimentally verify the effectiveness and superiority of the proposed method.The generalization performance of the proposed method is tested under the variable load condition and different signal-to-noise ratios(SNRs).The experimental results show that the average accuracy of the proposed method under different working conditions is 99.2%without adding noise.The accuracy under different working conditions from 0 to 1 HP is 100%.When the SNR is 0 dB,the average accuracy of the proposed method can still reach 98.7%under varying working conditions.Therefore,the bearing fault diagnosis method proposed in this paper is characterized by high accuracy,strong anti-noise ability,and generalization.Moreover,the proposed method can also overcome the influence of variable working conditions on diagnosis accuracy,providing method support for the accurate diagnosis of bearing faults under strong noise and variable working conditions.

基于Markov Chain的协议异常检测模型

本文介绍了基于Markov链的协议异常检测模型,此外,通过对MIT Lincoln实验室1999评估数据的分析,证明此模型的正确性和有效性。

基于MLP-ANN与Markov Chain的土地利用变化预测方法——以锡林郭勒盟为例

以北方草地典型地区—内蒙古锡林郭勒盟为案例区,在1995年到2000年的土地利用变化与驱动力分析的基础上,利用土地利用转换类型和驱动力模型,采用多层感知人工神经网络模型分析了各种土地利用类型未来的转换潜力;利用马尔可夫链模型,预测了2005和2010年土地利用格局。预测结果显示:高覆盖度草地减少幅度最大,中覆盖度草地减少相对和缓,高、中覆盖度草地的减少造成了未利用地和低覆盖度草地的增加,尤其是前者增加的幅度最大;从空间分布看,高覆盖度草地的减少集中在西北部地区,主要转变为中低覆盖度草地,中覆盖度草地的减少主要集中在西南部地区,其流向主要是以沙化土地为主的未利用地;案例研究表明,多层感知人工神经网络模型与马尔可夫链模型的结合与应用能够在很大程度上预测稳定驱动力作用下的土地利用变化趋势,从而为生态干预提供指导。

多重填补法Markov Chain Monte Carlo模型在有缺失值的妇幼卫生纵向数据中的应用

目的 针对妇幼卫生纵向数据的任意缺失模式,采用多重填补方法进行填补,探求最佳填补结果,以便对数据作进一步分析与研究。方法 运用SAS9.0 ,采用多重填补方法Markov China Monte Carlo(MCMC)模型对缺失数据进行多次填补并综合分析。结果 填补5次所得结果最优。结论 多重填补方法可以处理有缺失数据资料中的许多普遍问题,可提高统计效率,尤其是MCMC模型在处理复杂的缺失数据上,优势明显。

高等院校教师人才流动的Markov-chain预测模型

介绍并解析随机过程理论中的马尔科夫过程与马尔科夫链;针对高等院校教师人才流动变化过程,利用马尔科夫过程分析方法建立描述人员流动变化趋势的Markov-chain预测模型,详细阐述了模型的算法步骤.以某所高等院校教师人才流动的状态转移数据作为算例,运用新建立的预测模型,对该院校教师人才的流动趋势做出了预测分析.最后,将教师进修状态纳入分析范围,进行了教师职业生涯和职务发展趋势预测的深入分析.应用模型对实际算例的求解结果表明:Markov-chain预测模型及算法,叙述简洁、运算方便,为高等院校教师人才流动,乃至其他行业人才流动的预测提供了一种新的、有效的思路和方法.

基于RS-SPA-Markov chain的生物质气化站安全评价与预测模型研究

本文在资料收集、实地考察、专家评估的基础上,建立了相对通用的生物质气化站安全评价指标体系,引入了RS-SPA-Markov chain安全评价与预测模型。通过实例应用,证明了该模型应用于生物质气化站安全评价与预测的可行性和科学性,为生物质气化站安全评价与预测提供了一种新的途径。

基于Markov chain理论的科技成果转化的市场预测

科技成果成功转化的主要标志是其产品的市场畅销度。产品的畅销度由于受各种内外部不确定因素影响,具有随机不确定性。基于这种随机不确定性,运用Markovchain对其产品进行市场预测,并通过实证分析说明其有效性,为科技成果的转化提供具体可行的定量依据。

Auto-selection order of Markov chain for background sequences with chi-square test

Modeling non coding background sequences appropriately is important for the detection of regulatory elements from DNA sequences. Based on the chi square statistic test, some explanations about why to choose higher order Markov chain model and how to automatically select the proper order are given in this paper. The chi square test is first run on synthetic data sets to show that it can efficiently find the proper order of Markov chain. Using chi square test, distinct higher order context dependences inherent in ten sets of sequences of yeast S.cerevisiae from other literature have been found. So the Markov chain with higher order would be more suitable for modeling the non coding background sequences than an independent model.

Applicability of Markov chain-based stochastic model for bubbling fluidized beds

A Markov chain-based stochastic model （MCM） is developed to simulate the movement of particles in a 2D bubbling fluidized bed （BFB）. The state spaces are determined by the discretized physical cells of the bed, and the transition probability matrix is directly calculated by the results of a discrete element method （DEM） simulation. The Markov property of the BFB is discussed by the comparison results calculated from both static and dynamic transition probability matrices. The static matrix is calculated based on the Markov chain while the dynamic matrix is calculated based on the memory property of the particle movement. Results show that the difference in the trends of particle movement between the static and dynamic matrix calculation is very small. Besides, the particle mixing curves of the MCM and DEM have the same trend and similar numerical values, and the details show the time averaged characteristic of the MCM and also expose its shortcoming in describing the instantaneous particle dynamics in the BFB.

D-S理论和Markov链组合的桥梁性能退化预测研究

为准确预测桥梁性能退化,考虑到数据随机性和微小扰动发生状态跳跃,提出了一种D-S(Dempster-Shafer)证据理论和Markov链组合的桥梁性能退化组合预测模型和性能退化率的概念.该模型基于指数平滑(exponential smoothing,ES)方法获得新的预测数据序列,并利用Markov链和D-S理论不断进行优化,从而实现桥梁性能退化的组合预测.实际工程的应用结果表明:性能退化率可以直观地表征在梁性能退化的速度.其次,该模型的平均相对误差为1.54%,较于回归、灰色和模糊加权Markov链模型,精度分别提高了1.11%,0.88%和2.8%,而后验差比值为0.242,小于0.35;模型的标准差为9.021,相比其他模型分别减小了3.978,3.405和7.500,而变异系数为0.109,均小于其他模型,验证了组合预测模型在精度和稳定性方面的优越性,可为在役桥梁结构性能退化预测与维护提供理论基础.

基于Markov Chain Monte Carlo模型对医院调查资料中缺失数据的多重估算

目的探讨基于Markov Chain Monte Carlo(MCMC)模型的多重估算法在处理医院调查资料缺失数据中的应用。方法运用SAS9.2编写程序,在分析数据的分布类型和缺失机制的基础上,采用MCMC法对缺失数据进行多次填补和联合统计推断,分析多重估算法的优势。结果数据服从多元正态分布与随机缺失,采用MCMC法填补10次所得的结果最佳。结论多重估算既可反映缺失数据的不确定性,又可充分利用现有资料的信息、提高统计效率、对模型的估计结果更加可信,是处理缺失数据的有效方法。

基于改进Markov算法的电力线载波通信网络安全态势感知仿真研究

针对电力线载波通信网络安全态势感知单位运算时间较长且误差较大等问题,基于改进Markov算法研究一种新型通信网络安全态势感知方法。采用分区采集与降维运算数据预处理,去除电力线载波信号干扰因素。利用隶属关联矩阵挖掘网络安全要素特征,构建层次化Markov网络安全态势感知模型。利用BW算法寻找目标参数最优解,来确定感知目标点位置,缩短挖掘时间,提高感知精准度。经过试验验证,所提方法单位感知时间只有60~90 ms,多组并行感知均方误差不超过2%,表明所提方法能够满足电力线载波通信网络安全态势感知应用需求。

非线性广义时滞Markov跳变系统的H_(∞)滑模控制

研究了一类转移速率部分未知的广义时滞Markov跳变系统的H_(∞)滑模控制问题.首先,对广义时滞Markov跳变系统设计了积分型滑模面,并求出对应的等效控制器.之后,构建Lyapunov泛函,通过线性矩阵不等式方法得到闭环系统随机容许且满足H_(∞)性能γ的充分条件,运用加减项方法以及引入自由权矩阵,使得到的结果降低了保守性;对滑模力学分析,设计了滑模控制器,使得系统能在有限时间内到达滑模面上.最后,通过数值算例与仿真验证了理论的可行性.

Basic Lithofacies-Succession Model for the Wumishan Cyclothems: Their Markov Chain Analysis and Regularly Vertical Stacking Patterns in the Third-Order Sequences

The Mesoproterozoic Wumishan Formation in the Jixian section of Tianjin is a succession of 3300-m-thick carbonate strata formed in a period of about 100 Ma (1310±20 Ma-1207±10 Ma). In this succession of strata, the carbonate metre-scale cyclic sequences belonging to peritidal type with an approximately symmetrical lithofacies-succession are best developed. The wide development of 1:4 stacking patterns shows that these metre-scale cyclic sequences are genetically related to the short-eccentricity cycles, which are called the Wumishan cyclothems that could truly represent sedimentary cycles. Generally, massive and thick-bedded calcareous dolomites and dolomitic limestones of stromatolite biostromes and thrombolite bioherms constitute the central part of the Wumishan cyclothems. The lower and upper parts consist of tidal flat dolostones, sandy-muddy dolostone and the top part is composed of lagoonal facies dolomitic shales with a paleosol cap. Therefore, an approximately symmetrical lithofacies-succession is formed. Many features such as the clear deepening and shoaling vectors of cyclothems, and all kinds of marks of fresh-water diagenesis indicate that the Wumishan cyclothems are the product of autocyclic sedimentation governed by allocyclic high-frequency sea-level changes. The results of a Markov chain analysis reaffirm the existence of the lithofacies-succession model of the Wumishan cyclothems. The boundaries of the Wumishan cyclothems are marked by the instantaneous exposed punctuated surface, which leads to the discrepancy between the cyclothems and the parasequences of the sequence stratigraphy terminology system. It is difficult to form a judgment that the time span of the Milankovitch cycles in the Precambrian is certainly equal to that of the Phanerozoic, but the regularly vertical stacking patterns of the seventh-order rhythms, sixth-order cyclothems and fifth-order parasequence sets still indicate their consistency with the duration of the Milankovitch cycles in the Phanerozoic.

转移概率部分未知的离散时间Markov跳变系统Nash微分博弈

考虑到转移概率矩阵元素无法完全获悉,如何在转移概率部分未知的情境下研究离散时间Markov跳变系统Nash微分博弈是有待解决的问题之一,这一问题可以为转移概率部分未知的Markov跳变系统Nash微分博弈理论在管理问题上的应用提供理论支撑。基于此,本文首先研究单人博弈情形,即ε-次优控制问题,借助自由连接权矩阵和配方法,得到了ε-次优控制策略存在的充分性条件,并给出了成本函数上界的显式表达;然后延伸至双人博弈进行分析,得到了ε-次优Nash均衡策略存在的条件等价于求解双线性矩阵不等式和矩阵不等式的优化问题,并通过启发式算法求解优化问题得到ε-次优Nash均衡策略;最后通过数值算例证明了主要结论的有效性。