Attribute Reduction of Hybrid Decision Information Systems Based on Fuzzy Conditional Information Entropy

The presence of numerous uncertainties in hybrid decision information systems(HDISs)renders attribute reduction a formidable task.Currently available attribute reduction algorithms,including those based on Pawlak attribute importance,Skowron discernibility matrix,and information entropy,struggle to effectively manages multiple uncertainties simultaneously in HDISs like the precise measurement of disparities between nominal attribute values,and attributes with fuzzy boundaries and abnormal values.In order to address the aforementioned issues,this paper delves into the study of attribute reduction withinHDISs.First of all,a novel metric based on the decision attribute is introduced to solve the problem of accurately measuring the differences between nominal attribute values.The newly introduced distance metric has been christened the supervised distance that can effectively quantify the differences between the nominal attribute values.Then,based on the newly developed metric,a novel fuzzy relationship is defined from the perspective of“feedback on parity of attribute values to attribute sets”.This new fuzzy relationship serves as a valuable tool in addressing the challenges posed by abnormal attribute values.Furthermore,leveraging the newly introduced fuzzy relationship,the fuzzy conditional information entropy is defined as a solution to the challenges posed by fuzzy attributes.It effectively quantifies the uncertainty associated with fuzzy attribute values,thereby providing a robust framework for handling fuzzy information in hybrid information systems.Finally,an algorithm for attribute reduction utilizing the fuzzy conditional information entropy is presented.The experimental results on 12 datasets show that the average reduction rate of our algorithm reaches 84.04%,and the classification accuracy is improved by 3.91%compared to the original dataset,and by an average of 11.25%compared to the other 9 state-of-the-art reduction algorithms.The comprehensive analysis of these research results clearly indicates that our algorithm is highly effective in managing the intricate uncertainties inherent in hybrid data.

Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

Conditional Entropy of Partitions on Quantum Logic

A construction of conditional entropy of partitions on quantum logic is given,and the properties ofconditional entropy are investigated.

Entropy Formulation for Triply Nonlinear Degenerate Elliptic-Parabolic-Hyperbolic Equation with Zero-Flux Boundary Condition

In this note, we investigated existence and uniqueness of entropy solution for triply nonlinear degenerate parabolic problem with zero-flux boundary condition. Accordingly to the case of doubly nonlinear degenerate parabolic hyperbolic equation, we propose a generalization of entropy formulation and prove existence and uniqueness result without any structure condition.

One Parameter Family of N-Qudit Werner-Popescu States: Bipartite Separability Using Conditional Quantum Relative Tsallis Entropy

The conditional version of sandwiched Tsallis relative entropy (CSTRE) is employed to study the bipartite separability of one parameter family of N-qudit Werner-Popescu states in their 1:N-1 partition. For all N, the strongest limitation on bipartite separability is realized in the limit and is found to match exactly with the separability range obtained using an algebraic method which is both necessary and sufficient. The theoretical superiority of using CSTRE criterion to find the bipartite separability range over the one using Abe-Rajagopal (AR) q-conditional entropy is illustrated by comparing the convergence of the parameter x with respect to q, in the implicit plots of AR q-conditional entropy and CSTRE.

Formation condition of solid solution type high-entropy alloy

Formation condition of high-entropy alloys with solid solution structure was investigated. Seventeen kinds of the high-entropy alloys with different components were prepared, the influencing factors （the comprehensive atomic radius difference δ, the mixing enthalpy AH and the mixing entropy AS） of phase composition of the alloys were calculated, and the microstructure and phase compositions of alloys were analyzed by using SEM and XRD. The result shows that only the systems with δ≤2.77 and △H≥-8.8 kJ/mol will form high entropy alloy with simple solid solution. Otherwise, intermetallic compounds will exist in the alloys. So, selection of the type of element has important effects on microstructure and properties of high entropy alloys.

Analyses of an air conditioning system with entropy generation minimization and entransy theory

In this paper,based on the generalized heat transfer law,an air conditioning system is analyzed with the entropy generation minimization and the entransy theory.Taking the coefficient of performance（denoted as COP） and heat flow rate Qout which is released into the room as the optimization objectives,we discuss the applicabilities of the entropy generation minimization and entransy theory to the optimizations.Five numerical cases are presented.Combining the numerical results and theoretical analyses,we can conclude that the optimization applicabilities of the two theories are conditional.If Qout is the optimization objective,larger entransy increase rate always leads to larger Qout,while smaller entropy generation rate does not.If we take COP as the optimization objective,neither the entropy generation minimization nor the concept of entransy increase is always applicable.Furthermore,we find that the concept of entransy dissipation is not applicable for the discussed cases.

Entropy Assessment on Environmental Influence of Condense Heat in Recovery System in Air-Conditioning Refrigerating Machine

This paper presented an entropy evaluation method for the influences of condense heat recovery system on the environment.Aiming at the damage of the condense heat to the environment,an entropy of resource loss and an emission entropy from the condense heat recovery system in the air conditioning refrigerating machine were introduced.For the evaluation of the entropies,we developed a new algorithm for the parameter identification,called the composite influence coefficient,based on the Least Squares Support Vector Machine method.By simulation,the numerical experiments shows that the Least Squares Support Vector Machine method is one of the powerful methods for the parameter identification to compute the damage entropy of the condense heat,with the largest training error being-0.025(the relative error being-3.56%),and the biggest test error being 0.015(the relative error being 2.5%).

Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow

The Riemann problem for the Aw-Rascle model in the traffic flow with the Delta initial data for the Chaplygin gas is studied. The solutions are constructed globally under the generalized Rankine-Hugoniot relations, the δ-entropy conditions, and the generalized δ-entropy conditions. A new Delta wave, which is called a primary Delta wave, is defined in some solutions. The primary Delta wave satisfies the generalized Rankine- Hugoniot relations and the generalized δ-entropy conditions. It generates initially from the Delta initial data, which either evaluates a Delta wave, whose weight becomes stronger and stronger, or disappears at a finite time.

An Information Entropy-Based Methodology to Construct the Avulsion Threshold in the Tail Reach of the Estuarine Alluvial Plain

Channel avulsion is a natural phenomenon that occurs abruptly on alluvial river deltas,which can affect the channel stability.The causes for avulsion could be generally categorized as topography-and flood-driven factors.However,previous studies on avulsion thresholds usually focused on topography-driven factors due to the centurial or millennial avulsion timescales of the world’s most deltas,but neglected the impacts of flood-driven factors.In the current study,a novel demarcation equation including the two driven factors was proposed,with the decadal timescale of avulsion being considered in the Yellow River Estuary(YRE).In order to quantify the contributions of different factors in each category,an entropy-based methodology was used to calculate the contributing weights of these factors.The factor with the highest weight in each category was then used to construct the demarcation equation,based on avulsion datasets associated with the YRE.An avulsion threshold was deduced according to the demarcation equation.This avulsion threshold was then applied to conduct the risk assessment of avulsion in the YRE.The results show that:two dominant factors cover respectively geomorphic coefficient representing the topography-driven factor and fluvial erosion intensity representing the flood-driven factor,which were thus employed to define a two dimensional mathematical space in which the demarcation equation can be obtained;the avulsion threshold derived from the equation was also applied in the risk assessment of avulsion;and the avulsion threshold proposed in this study is more accurate,as compared with the existing thresholds.

一种新的油气管道泄漏信号检测方法研究

针对管道模式识别模型效率低下、准确率不足的问题,提出一种新的管道泄漏检测方法。首先利用信号能量熵突变情况对泄漏引起的信号跳变进行有效捕捉,其次利用变分模态分解(VMD)进行去噪处理,还原信号真实动态特性。基于熵特征提取去噪信号的动态特征段,并将提取的特征向量输入改进差分进化算法(IDE)优化的支持向量机(SVM)识别模块种,实现泄漏信号的辨识。实验结果表明,与GA-SVM和PSO-SVM方法相比,IDE-SVM方法有效提高了分类识别准确率,准确率达到96.6667%。

基于多核模糊条件熵的多类型混合数据属性约简算法

对数据进行有效属性约简是数据挖掘中一个具有挑战性的任务。当前,粗糙集理论是构造属性约简的一种常用方法。然而,现有的属性约简方法都侧重于单类型的数据,对现实环境下多类型混合的数据并不适用。为了解决这一问题,提出一种多核模糊条件熵的多类型混合数据属性约简算法。首先,针对标记型、数值型、区间型和集值型混合的多类型数据,提出了一种多核模糊相似关系。然后,基于这种多核模糊相似关系,定义了一种多核模糊条件熵模型,并讨论了它的单调性和有界性。最后,利用多核模糊条件熵的单调性提出了一种多类型混合数据的属性约简算法。通过UCI数据集的实验分析验证了该算法的有效性。

中等规模城市居民住房条件的时空分异格局及驱动机制——以肇庆市为例

中等规模城市住房发展的不充分不平衡问题长期被学术界所忽视。文章基于肇庆市第六次和第七次全国分乡镇街道人口普查数据,构建肇庆市居民住房条件评价体系,分析2010—2020年肇庆市居民住房条件的时空分异格局、空间相关特征和驱动机制。结果表明:1)2010—2020年,肇庆市居民住房条件的空间差异特征发生明显变化,表现为高分区域由东南向西北转移;2)肇庆市居民住房条件总体呈现显著的空间集聚特征,10年间住房总体条件得分的空间集聚度变化不大,建成年代、建筑结构和住房生活设施得分的空间集聚度大幅下降;3)2020年,城镇居民和乡村居民的住房条件呈现不同的空间分异格局,乡村住房的人均建筑面积子系统主导该市所有居民住房条件的空间分异格局;4)驱动机制方面,早期的城市形态构成肇庆市住房条件空间格局的历史基础,政府政策与规划是塑造空间格局演变的关键动力,住房市场的过滤效应进一步强化既定的空间格局。

基于改进信息熵的直接刀具状态监测设备部署

在不拆刀情况下,基于机器视觉的在线刀具状态监测系统可完成刀具磨损测量和状态评估,但与在线捕获刀具图像质量息息相关的系统部署参数选择却鲜有研究.为解决上述问题,本文构建基于改进信息熵的多项式回归模型以实现刀具状态监测系统的最优部署.首先,使用自适应阈值方法去除捕获刀具图像中背景要素干扰,并通过信息熵指标评估图像中刀具磨损区域的成像质量;然后,构建相机工作距离、曝光时间与所提出评价指标之间的多项式回归模型以描述部署参数与提出评价指标的映射关系;最后,应用最小二乘法求取多项式模型系数获得最优部署参数.在确保自变量的因子水平涵盖最优部署参数情况下设计正交实验,实验结果表明:提出的评价指标与工作距离、曝光时间等部署参数之间均存在主效应关系,符合光学成像系统的变化规律;与支持向量机、决策树和K近邻(K-nearest neighbor,KNN)算法等非线性回归预测模型相比,三次多项式回归模型预测误差最小,其平均绝对误差、均方误差、均方根误差分别为0.022631,0.00068,0.026069;在多项式回归模型求解的最优部署参数下,所捕获的刀具图像的测量精度达到96.76%,提高0.74%,满足刀具状态监测的精度要求.

基于自信息熵的直觉模糊决策系统的属性约简

针对在直觉模糊集中,利用下近似构建的约简只考虑了下近似而忽略了上近似,从而导致一些信息丢失的问题,基于直觉模糊集的上、下近似提出了3种熵度量,并将其应用于直觉模糊决策信息系统的约简之中。在直觉模糊决策信息系统上定义用于描述直觉模糊关系的3种不确定性度量,分别为平均决策指数、平均安全决策指数以及平均风险决策指数,并在此基础上依次提出了条件信息熵、条件粗糙熵和自信息熵,基于自信息熵给出了相应的约简定义以及属性约简算法。在多个数据集上的实验表明,所提出的属性约简算法与其他算法相比,约简结果更具有优越性以及鲁棒性。

最大化广义瑞利熵在列车空调制冷剂充注量诊断中应用

[目的]利用机器学习方法对列车空调制冷剂充注量的诊断中,经常出现许多特征,如何选择特征成为诊断中两难的抉择。特征选择过多,算法资源开销巨大;特征选择过少,则不能很好地学习故障信息,导致诊断模型的效果不好。目前,在特征选择中,有一个比较常用的方法,即PCA(主成分分析),还有一个引用次数比较少的为最大化瑞利熵,2个皆存在特征过多导致的算法资源开销过大问题。为减少资源开销及比较二者优劣,特开展本研究。[方法]选用比较经典的支持向量机和均值聚类模型作比较,同时利用小样本历史数据构造降维算法而不是利用全体样本构造最大化瑞利熵的降维算法,同样是为了减少资源开销,属于对算法的改进。比较基于小样本历史数据的最大化广义瑞利熵降维和常用的PCA降维方式在均值聚类和支持向量机模型的f1得分、准确率和时间开销上的优劣。[结果及结论]结果表明,最大化广义瑞利熵的支持向量机的故障诊断和探测时间资源开销只有原始数据训练支持向量机模型的3%,无论是均值聚类还是支持向量机在使用最大化瑞利熵的投影后的数据,测试数据准确率比其他模型更接近100%。

基于邻域量化容差条件熵增量式更新的网络入侵检测方法

网络入侵检测系统是网络信息安全防护的重要防御工具,而复杂的、冗长的网络入侵行为特征严重影响了网络入侵检测的效果。针对网络入侵检测中信息量增长迅速、数据不完备的现实问题,提出一种基于邻域量化容差条件熵增量式更新的特征选择算法。首先,在邻域量化容差粒计算的基础上,结合条件熵在刻画特征不确定性、对特征之间的相关或依赖程度方面的显著特性,研究了邻域量化容差条件熵的增量式更新机制;然后,基于该更新机制提出动态数据库增量式更新的特征选择算法;最后,通过数据实验分析验证了所提出的算法能有效提高不完备信息系统特征选择的计算效率。新提出的算法在网络入侵检测实例应用中体现的计算复杂度及虚警率低的优势,表明其可为网络信息安全防护提供有效可行的具体方法。

基于模糊粒度条件熵与改进萤火虫算法的特征选择方法

提出了一种基于模糊粒度条件熵与改进萤火虫算法(firefly algorithm,FA)的特征选择方法FS_FGCEIFA。将模糊粗糙集中的知识粒度与λ-条件熵结合,提出模糊粒度条件熵这一新的信息熵模型;将模糊粒度条件熵应用于FA中,提出一种基于模糊粒度条件熵的适应度函数;采用引力搜索算法中粒子惯性质量和万有引力的计算策略来调整FA中萤火虫的亮度和吸引力,并且将基于引力搜索的自适应步长因子融入FA的位置更新中。在多个UCI数据集以及软件缺陷预测数据集上的实验表明,FS_FGCEIFA能够获得更好的分类性能。

基于模糊综合评价的户式空调系统优选方案评估方法

针对户式空调系统性能常用评价方法存在评价指标不全面、评价过程复杂及评价结果主观性强等不足,提出1种户式空调系统性能模糊综合评价方法。考虑空调行业绿色低碳的发展要求,在原有评价指标的基础上增加室外环境及技术特性相关指标,采用层次分析法建立户式空调系统性能评价指标体系,采用专家调查法和信息熵法分别对指标权重进行赋值和修正,采用分布函数法和等级比重法分别对定量和定性指标进行隶属度计算,最后进行模糊综合评价。以多联机和热湿分控2种典型户式空调系统为例,分别采用层次分析法和本文方法进行评价,验证本文方法的科学合理性。结果表明:2种评价方法对多联机和热湿分控方案的综合评定等级均为Ⅱ级,对于层次分析法,综合评价值分别为53.72,53.43,2种方案的评价结果几乎一致,2种方案没有明显优劣,难以为空调选型提供参考;对于本文方法,2种方案的评价结果差值明显,可为空调选型提供参考,这是因为本文方法的评价指标更全面,且在模糊评价法和信息熵法的作用下完成复杂问题的量化,可弥补评价过程复杂和评价结果主观性强的不足。

复合多尺度注意熵在旋转机械多工况损伤识别中的应用

针对传统旋转机械损伤识别方法存在模型精度低和抗噪性差的问题,提出了一种基于复合多尺度注意熵(CMATE)和随机森林(RF)的旋转机械多工况损伤识别方法。首先,提出了一种新的测量时间序列复杂度的非线性动力学工具——复合多尺度注意熵;然后,利用CMATE提取旋转机械振动信号的损伤特征,其表征了旋转机械不同工况下的损伤特性;接着,将损伤特征输入至基于随机森林构造的多类别分类器中,进行了损伤识别;最后,采用滚动轴承-齿轮箱、齿轮箱和离心泵3种旋转机械数据集,并分别构造了9种工况和20种工况的多工况损伤数据集,对该损伤识别方法进行了实验研究。研究结果表明:该旋转机械损伤识别方法分别取得95%、97%和100%的识别准确率,在准确率和特征提取效率两方面优于其他的非线性动力学工具;并且在0 dB、1 dB、2 dB和3 dB这4种不同信噪比的噪声干扰下,依然取得了不错的损伤识别结果,证明了该模型具有可观的抗噪性;同时,该损伤识别方法能够稳定地识别旋转机械的不同负载和转速下的损伤,平均识别准确率分别达到了97.2%和93.5%,具有较好的实际应用潜力。