Rough function model and rough membership function

Two pairs of approximation operators, which are the scale lower and upper approximations as well as the real line lower and upper approximations, are defined. Their properties and antithesis characteristics are analyzed. The rough function model is generalized based on rough set theory, and the scheme of rough function theory is made more distinct and complete. Therefore, the transformation of the real function analysis from real line to scale is achieved. A series of basic concepts in rough function model including rough numbers, rough intervals, and rough membership functions are defined in the new scheme of the rough function model. Operating properties of rough intervals similar to rough sets are obtained. The relationship of rough inclusion and rough equality of rough intervals is defined by two kinds of tools, known as the lower （upper） approximation operator in real numbers domain and rough membership functions. Their relative properties are analyzed and proved strictly, which provides necessary theoretical foundation and technical support for the further discussion of properties and practical application of the rough function model.

Pseudo-Semi-Overlap Functions-Based Fuzzy Rough Sets Applied to Image Edge Extraction

As an extension of overlap functions, pseudo-semi-overlap functions are a crucial class of aggregation functions. Therefore, (I, PSO)-fuzzy rough sets are introduced, utilizing pseudo-semi-overlap functions, and further extended for applications in image edge extraction. Firstly, a new clustering function, the pseudo-semi-overlap function, is introduced by eliminating the symmetry and right continuity present in the overlap function. The relaxed nature of this function enhances its applicability in image edge extraction. Secondly, the definitions of (I, PSO)-fuzzy rough sets are provided, using (I, PSO)-fuzzy rough sets, a pair of new fuzzy mathematical morphological operators (IPSOFMM operators) is proposed. Finally, by combining the fuzzy C-means algorithm and IPSOFMM operators, a novel image edge extraction algorithm (FCM-IPSO algorithm) is proposed and implemented. Compared to existing algorithms, the FCM-IPSO algorithm exhibits more image edges and a 73.81% decrease in the noise introduction rate. The outstanding performance of (I, PSO)-fuzzy rough sets in image edge extraction demonstrates their practical application value.

Function S-Rough sets and its applications

Based on S-rough sets（singular rough sets）, this paper presents function S-rough sets （function singular rough sets）and its mathematical structures and features. Function S-rough sets has two forms： function one direction S-rough sets （function one direction singular rough sets） and function two direction S-rough sets （function two direction singular rough sets）. This paper advances the relationship theorem of function S-rough sets and S-rough sets. Function S-rough sets is the general form of S-rough sets, and S-rough sets is the special ease of function S-rough sets. In this paper, applications of function S-rough sets in rough law mining-discovery of system are given. Function S-rough sets is a new research direction of rough sets and rough system.

Function S-rough sets and mining-discovery of rough law in systems

Function S-rough sets （function singular rough sets） is defined on a -function equivalence class [u]. Function S-rough sets is the extension form of S-rough sets. By using the function S-rough sets, this paper gives rough law generation model of a-function equivalence class, discussion on law mining and law discovery in systems, and application of law mining and law discovery in communication system. Function S-rough sets is a new theory and method in law mining research.

Rough Integrals Generated by Function Rough Sets

The concepts of the lower approximation integral,the upper approximation integral and rough integrals are given on the basis of function rough sets.Based on these concepts,the relation of the lower approximation integrals,the relation of the upper approximation integrals,the relation of rough integrals,and the double median theorem of rough integrals are discussed.Rough integrals have finite contraction characteristic and finite extension characteristic.

A Method of Gene-Function Annotation Based on Variable Precision Rough Sets

It is very important in the field of bioinformatics to apply computer to perform the function annotation for new sequenced bio-sequences. Based on GO database and BLAST program, a novel method for the function annotation of new biological sequences is presented by using the variable-precision rough set theory. The proposed method is applied to the real data in GO database to examine its effectiveness. Numerical results show that the proposed method has better precision, recall-rate and harmonic mean value compared with existing methods.

Research on the acoustic scattering function and coherence properties from rough seafloor based on finite element model

Acoustic scattering from a rough sea bottom is recognized as a main source of reverberation. In this study, scattering properties from a layered bottom were exploited based on the finite element model. The scattering strength and loss from the layered rough seabed were investigated by ensembling the realizations of rough interface. They were found to be dependent on the thickness of sediment, and interference was significant in the case of thin sediment. Through verification of the finite element model, the scattering loss could be evaluated using the Eckart model with a proper sound speed in the thick sediment. The multiple scattering effect on the sound field was also exploited. It revealed that the effect depended strongly on the bottom type.

Bidirectional reflectance one-dimensional rough distribution function modeling of surface in the microwave band

In this study, the bidirectional reflectance distribution function （BRDF） of a one-dimensional conducting rough surface and a dielectric rough surface are calculated with different frequencies and roughness values in the microwave band by using the method of moments, and the relationship between the bistatic scattering coefficient and the BRDF of a rough surface is expressed. From the theory of the parameters of the rough surface BRDF, the parameters of the BRDF are obtained using a genetic algorithm. The BRDF of a rough surface is calculated using the obtained parameter values. Further, the fitting values and theoretical calculations of the BRDF are compared, and the optimization results are in agreement with the theoretical calculation results. Finally, a reference for BRDF modeling of a Gaussian rough surface in the microwave band is provided by the proposed method.

Effect of the Illuminating Point Spread Function and Roughness on the Speckle Correlation Field

Under conditions differing from those subjected for central limit theorem, the spatial autocorrelation function of speckle pattern resulting from illuminated rough surface is investigated. Its dependence on different illuminating apertures and the average of the roughness heights is presented theoretically and experimentally. The experiments were carried out using a set of circular and square apertures having different sizes. The results indicate that, increasing the size of the illuminating aperture leads to a decrease in the width of the main lobe of the spatial autocorrelation function.

Function S-rough sets and two law forecast

Function S-rough sets has the properties of dynamics, heredity, and memory. Function S-rough sets is penetrated and crossed with the issue of economic law forecast, then a new forecast model based on function S-rough sets namely the two law forecast model is proposed, which includes upper law forecast model and lower law forecast model; and its＇ implement algorithm is given. Finally, the validity of the model is demonstrated by the forecast for region economic development of Hainan Province.

K9光学元件的锥形约束射流抛光流场与加工实验研究

提出了锥形约束射流抛光的加工方法,将原本垂直的细小射流约束成几乎平行于工件表面的环形射流。使用Fluent软件对抛光流场进行数值分析,根据Preston方程建立了材料去除函数模型;并以K9玻璃为加工对象,利用自主设计的锥形约束射流抛光平台进行加工实验。结果表明,锥形约束射流抛光方法法向最大速度比切向最大速度小63.9%,从而减少射流在垂直于工件表面方向的冲击损伤;锥形约束射流抛光后,K9玻璃表面粗糙度在加工区域内呈“V”型分布,其算数平均粗糙度(Ra)值从95.40 nm降至14.52 nm,表面质量得到明显提高。锥形约束射流抛光主要依靠射流沿工件表面的剪切力,不仅有效减小了射流法向冲击力,对射流的约束还减小了射流束的发散;确定的表面去除函数表明该方法有望实现确定性抛光;另外,环形的射流出口提高了射流抛光的效率。

基于平均型聚合函数的多粒度模糊粗糙集

多粒度模糊粗糙集(multi-granulation fuzzy rough set,MGFRS)是一种重要的粗糙集模型。乐观多粒度模糊粗糙集和悲观多粒度模糊粗糙集分别给出了被描述对象的两种极端描述。从数据聚合角度看,将不同粒度值合并为单一粒度值时,乐观MGFRS采用的是取小算子,悲观MGFRS采用的是取大算子。将取小与取大算子拓展为一般的平均型聚合算子,提出了一种新的多粒度模糊粗糙集模型:基于平均型聚合函数的多粒度模糊粗糙集(multi-granulation fuzzy rough set model on the base of average aggregate function,MFA)模型。研究了MFA模型的基本性质,给出了MFA模型与乐观和悲观多粒度模糊粗糙集的关系。同时,基于MFA模型,提出了基于平均型聚合算子的粗糙近似集模型。

基于FSRce模型的机电产品绿色概念设计方案生成方法

针对部分机电产品在概念设计阶段未综合考虑客户和环境的需求,进而影响产品详细设计的问题,提出了一种基于功能—结构—客户和环境需求(function‒structure‒requirements of customer and environment,FSRce)模型的机电产品绿色概念设计方案生成方法。首先,从案例库中选择合适的功能和结构对现有产品设计树中的节点进行扩展和关联;同时通过数据挖掘、专家打分等方法获得产品的客户和环境需求重要度,以构建基于FSRce模型的产品概念设计空间。然后,先利用加权区间粗糙数法对客户和环境需求重要度进行分析,得到需求相对重要度,再运用模糊质量功能展开(fuzzy quality function deployment,FQFD)将需求相对重要度转化为产品的工程特性权重。最后,利用物元理论构建基于工程特性的产品物元域和各结构物元集,并结合工程特性权重得到各结构的满意度分值,通过比较满意度优选得到满足客户和环境需求的产品概念设计方案。以某小型工业吹风机为例,基于上述方法对其概念设计方案进行优化。相比于原始方案,优化后的吹风机在能源消耗上降低了15.38%,在碳排放上降低了15.32%,且客户满意度提高了44.66%,由此验证了所提出方法的可行性与有效性。所提出的方法为机电产品概念设计方案的生成提供了一种新思路,能更好地辅助设计人员实现对机电产品的绿色设计。

Rough集理论:现状与前景

经典逻辑中只有真、假二值,但实际上有大盆含糊现象存在于宾和假二值之间,因此,长以来许多逻辑学家和哲学家就致力于研究含糊概念。早在1904年谓词逻辑的创始人G.

Rough函数依赖及其推理机制

在引入 Rough函数依赖的基础上 ,提出了先行上、下冗余因子及结果上、下冗余因子的概念 ,研究了 Rough函数依赖的性质和推理规则 ,最后分析了 Rough函数依赖与函数依赖。

大气湍流下部分相干涡旋光束经粗糙目标回波特性

利用广义Huygens-Fresnel原理和随机高斯粗糙面模型,研究部分相干高斯-谢尔模型涡旋光束的回波特性,通过特殊积分推导出部分相干涡旋光束经随机粗糙面散射后到达接收端的交叉谱密度函数和光强解析式,并进行仿真分析。结果表明:随着拓扑荷数、束腰半径和相干长度的增加,光强自相关函数曲线下降的越来越陡峭;在强湍流环境下,自相关函数衰减越来越严重;内尺度会影响光强自相关函数,并且随着内尺度的增大而衰减严重,外尺度对其影响作用不大;随着粗糙目标相干长度的增大,光强自相关函数的半峰宽值逐渐趋增大。

一种基于Rough Set的启发式属性约简算法

属性约简的目的在于减少条件属性中不必要属性的数目,是知识发现中的关键问题之一。本文提出了一种改进的基于Rough集的启发式算法(IMSA),定义了新的启发函数(WSH)。这个函数考虑了所有隐藏规则集的质量,并且考虑了相关规则集的权重。在算法本身的时间复杂度没有增加的前提下,能够解决MSA算法遇到多个相同MSH值时无法处理的情况。实验分析表明,该算法是有效的。

基于Rough集理论的模糊神经网络构造方法

提出了在模糊神经网络中使用Rough集理论进行网络结构设计的方法。由于Rough集理论有强大的数值分析能力 ,而模糊神经网络具有准确的逼近收敛能力和较高的精度 ,所以通过两者的结合 ,可以得到一种可理解性好、计算简单、收敛速度快的神经网络模型。这种网络构造方法的主要过程为 :首先 ,利用Rough集理论对给定数据集进行规则获取 ;然后 ,根据这些规则构造模糊神经网络各层的神经元个数及相关参数初始值 ;最后 ,用BP算法迭代求出网络的各种参数 ,完成网络的设计。给出了一个二维非线性函数拟合的实例 。

覆盖广义Rough集中的隶属关系

对覆盖广义Rough集中的隶属关系、隶属函数进行了定义,并利用隶属函数定义了集合的Rough包含与Rough相等,得到一些与Paw lak的Rough集不同的性质。

基于(I,O_(s))-模糊粗糙集的图像边缘提取和特征选择应用

首先,利用半重叠函数和模糊粗糙集,构造了(I,O_(s))-模糊粗糙集模型,提高了模型的灵活性和适应性;其次,将该模型与模糊C-均值算法相结合,提出了一种新的图像边缘提取算法,该算法在较低引入率的情况下,能够提取到完整的图像边缘;最后,基于(I,O_(s))-模糊粗糙集模型,提出了一种新的特征选择算法,相较于传统的特征选择算法,该算法在保持高分类精度的情况下,可以选择更少的属性条件.实验证明,基于(I,O_(s))-模糊粗糙集模型的算法具有可行性和有效性,可以为相关研究和领域提供支持.