L-Fuzzy Rough Set Based on Complete Residuated Lattice

Residuated lattice is an important non-classical logic algebra, and L-fuzzy rough set based on residuated lattice can describe the information with incompleteness, fuzziness and uncomparativity in information systems. In this paper, the representation theorems of L-fuzzy rough sets based on residuated lattice are given. The properties and axiomatic definition of the lower and upper approximarion operators in L-fuzzy rough sets are discussed.

Rough Set Theory over Fuzzy Lattices

Rough set theory, proposed by Pawlak in 1982, is a tool for dealing with uncertainty and vagueness aspects of knowledge model. The main idea of rough sets corresponds to the lower and upper approximations based on equivalence relations. This paper studies the rough set and its extension. In our talk, we present a linear algebra approach to rough set and its extension, give an equivalent definition of the lower and upper approximations of rough set based on the characteristic function of sets, and then we explain the lower and upper approximations as the colinear map and linear map of sets, respectively. Finally, we define the rough sets over fuzzy lattices, which cover the rough set and fuzzy rough set,and the independent axiomatic systems are constructed to characterize the lower and upper approximations of rough set over fuzzy lattices,respectively,based on inner and outer products. The axiomatic systems unify the axiomization of Pawlak’s rough sets and fuzzy rough sets.

Logical Properties of Lattice Filter of Lattice Implication Algebra

Some new properties of lattice filters are presented based on the order-preserving mapping and lattice homomorphism, and two necessary and sufficient conditions for lattice filters under the chain type are given. Then, the relations between lattice filter and lattice implication algebras （LIAs）, i. e., the relations between lattice filter and LIA-filters, and the related properties are investigated. In addition, three necessary and sufficient conditions for LIA-filters are discussed. The obtained results may serve as some theoretical supports to lattice-valued logical system.

A study on distributive and modular lattice ordered fuzzy soft group and its duality

Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.

Lattice of Finite Group Actions on Prism Manifolds

The set of finite group actions (up to equivalence) which operate on a prism manifold M, preserve a Heegaard Klein bottle and have a fixed orbifold quotient type, form a partially ordered set. We describe the partial ordering of these actions by relating them to certain sets of ordered pairs of integers. There are seven possible orbifold quotient types, and for any fixed quotient type we show that the partially ordered set is isomorphic to a union of distributive lattices of a certain type. We give necessary and sufficent conditions, for these partially ordered sets to be isomorphic and to be a union of Boolean algebras.

The Existence of the Complete and Completely Distributive Lattices

The existence of some lattices and the lattice having the smallest set of generating elements are important in lattice theory. In this paper by means of the relations of the intrinsic topologies and admissible topology of a lattice,we prove there not exists the in flute complete and completely distributive lattice which has finite dimension.A complete boolean lattice B possesses the smallest set of generating elements iff B is completely distributive.

Lattice Theory for Finite Dimensional Hilbert Space with Variables in Z_d

In this work, join and meet algebraic structure which exists in non-near-linear finite geometry are discussed. Lines in non-near-linear finite geometry ?were expressed as products of lines in near-linear finite geometry ?(where?p?is a prime). An existence of lattice between any pair of near-linear finite geometry ?of ?is confirmed. For q|d, a one-to-one correspondence between the set of subgeometry ?of ?and finite geometry ?from the subsets of the set {D(d)}?of divisors of d?(where each divisor represents a finite geometry) and set of subsystems {∏(q)}?(with variables in Zq) of a finite quantum system ∏(d)?with variables in Zd?and a finite system from the subsets of the set of divisors of d?is established.

Research on global form deviations for spiral bevel gear based on latticed measurement

In order to improve the machining ac cu racy of spiral bevel gear,difference surface was adopted to characterize its gl obal form deviations quantifiably and correct its deviations.The theoretical to oth surface model of spiral bevel gear was built,and the actual tooth surface o f spiral bevel gear had been got by using latticed measurement.The equation of difference surface which can characterize the actual tooth surface deviation s was built by means of mathematical method in combination with measurement prin ciple.The quantitative mathematical relationship between the actual tooth surfa ce deviations of spiral bevel gear and the corrected values of the machine-sett ing parameters had been referred,and the theoretical correction formula of the global form deviations had been got by the least square method.Finally,the pinion of spiral bevel gear in the automobile rear axle has been set for an exam ple to account for the effectiveness of the deviation correction by use of the d ifference surface method.

基于LBM的泡沫金属与翅片相变储能系统性能对比分析

为了研究翅片和泡沫金属铜对相变储能系统性能的影响,使用四参数随机生长法(QSGS)构建了孔隙密度(PPI)分别为20PPI、30PPI的泡沫铜复合相变材料模型,并构建了等铜质量的翅片相变材料模型。在此基础上,采用格子玻尔兹曼(LBM)数值模拟方法对相变材料(PCM)的储/放热过程进行了数值模拟,基于努塞尔数、液相率、PCM流动速度、PCM熔化/凝固时间对比分析了添加翅片以及添加泡沫金属结构对相变材料换热性能的影响。结果表明,在储热过程中,由于泡沫金属的存在会抑制熔化过程中对流换热的发展,双翅片结构的努塞尔数高于泡沫金属结构,熔化时间更短,相比于20PPI、30PPI泡沫铜复合相变材料分别缩短了28.55%、17.5%;在放热过程中,泡沫金属的存在会增加热传导面积,泡沫金属结构的凝固速度高于翅片结构,30PPI泡沫金属结构的凝固时间相比于翅片、20PPI泡沫铜复合相变材料分别缩短了65.80%、20.24%。综合考虑储放热两个过程,30PPI泡沫金属结构的总储放热时间最短,相比于翅片、20PPI泡沫铜复合相变材料分别缩短了27.81%、15.32%。在耗费相同金属材料的条件下,采用泡沫结构是更为有效的提升储能效率的手段。

基于改进QSGS-LBM法的各向异性重构土体的渗流模拟

为解决传统四参数随机生长(quartet structure generation set, QSGS)方法重构模型与真实土体情况不符的缺陷,提出一种改进的QSGS方法,在综合考虑各向异性、孔隙率、土体颗粒大小情况下构建各向异性多孔介质模型.采用两点自相关函数法验证模型的有效性,并结合格子玻尔兹曼方法自编Matlab程序来模拟细观渗流过程.实验发现,各向同性模型和土体CT切片的两点相关系数最大差值是各向异性模型的2.5倍以上,且流体粒子在孔道中线处的渗流速度最大,达到0.03,在孔壁处渗流速度接近于0.结果表明,各向异性模型在孔隙结构和空间分布上更接近真实土体情况,流体在渗流后期出现大孔隙优先流现象和指进现象.

单纯形格点剖分下的混料型数据的分类算法

为了实现混料型数据的分类与识别,提出一类单纯形剖分算法.首先给出了混料系统和置换点集的概念,然后提出了两类正规单纯形剖分方法,进而对混料型数据进行分类识别,通过实例验证,单纯形剖分方法对于混料数据的分类是有效的.

基于格子Boltzmann方法的地埋管管群换热的模拟研究

土壤结构和地下水通常会影响地埋管换热器的传热,本文将利用随机四参数生成法建立双分布函数格子Boltzmann模型,对有渗流条件下地埋管管群换热器与饱和土壤多孔介质的换热情况进行了模拟,分析了影响埋管外土壤平均温度的主要因素。研究表明,土壤热传导特性主要受土壤孔隙度、地下水渗流速度和土壤骨架导热系数k s的影响。本文的研究结论对考虑土壤渗流的地下换热器的设计具有一定的指导意义。

基于AVX512的格密码高速并行实现

量子计算的迅速发展可能对当前广泛使用的公钥密码算法造成严重威胁。格密码因优秀的抗量子安全性和高效的计算效率在后量子密码中占据重要地位。美国国家标准技术研究院于2022年5月公布4个后量子密码标准,其中3个是格密码算法,Kyber算法便是其中之一。随着后量子密码标准的确定,Kyber算法高效实现的需求日益增加。基于512位高级向量扩展(AVX512),对Kyber算法进行优化与高速并行实现。使用惰性模约减、优化的蒙哥马利模约减及优化的快速数论变化等技术,充分利用计算机的存储空间,减少大量不必要的模约减操作,提高多项式计算的效率与并行性。采用冗余比特技术,增强多项式抽样过程中比特的并行处理能力。通过AVX512的512 bit位宽和8路并行实现哈希运算,并对其产生的伪随机比特串进行合理调度,充分发挥并行性能。基于AVX512指令集高速并行实现Kyber上的多项式计算和抽样,并进一步实现整个Kyber公钥加密方案。性能测试结果表明,与C语言实现相比,基于AVX512实现的密钥生成和加密算法获得了10~16倍的加速,解密算法获得了约56倍的加速。

基于“离位”点阵预成型体ES-T300/GT910复合材料的工程化制备及性能研究

采用离位“点阵”技术,制备预成型织物ES-T300/GT910复合材料,设置粉粒粒径、挖板辊速度,收卷速度为影响因素,采用正交设计L 9(34)对工艺优化,并对基本力学性能与进行了测试。结果显示:定型剂粉末的粒径为80目、挖板辊速度比为0、收卷速度为0.2 m/min时可以获满意的定型剂质量分数(5.37±0.09)%;“离位”ES-T300/GT910预定型织物回弹性能良好,力学性能良好。离位“点阵”ES-T300/GT910预定型复合材料可以达到工程化制备的标准,综合性能良好。

非均质点阵结构材料性能快速预测方法研究

随着智能设计方法和先进制造技术的快速发展,高端装备呈现出智能化、轻量化、多功能化、仿生化和制造一体化等发展趋势。虽然点阵结构具有轻质高强、减振降噪、抗冲击吸能等优异性能,然而其一直存在微观建模复杂且性能表征分析耗时的难题。为此,本文提出了一种基于切割水平集的非均质点阵微结构建模与数据驱动的材料性能快速预测方法。首先,每个微结构原型由一个水平集函数隐式表示,多个微结构原型组成一个复合点阵微结构,通过改变微结构原型的类型和数量可组合成多种非均质微结构构型。然后,采用均匀化理论计算点阵微结构的等效弹性矩阵并生成数据集,并通过神经网络建立其切割高度变量到等效弹性矩阵与体积分数之间的映射,所得代理模型可快速预测出点阵微结构的材料性能参数,从而替代昂贵的均匀化计算。实验结果表明,本文提出的预测方法可精确表征非均质点阵微结构,构建的代理模型可大幅减少点阵微结构性能计算成本,且具有较高的精度和鲁棒性。

BEST APPROXIMATION BY DOWNWARD SETS WITH APPLICATIONS

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X

Realization of Rough Set Approximation Toplogical Operations Based on Formal Concept Analysis

There is an intimate correlation between rough set theory and formal concept analysis theory, so rough set approximations can be realized by means of formal concept analysis. For any given multiple valued information system, the realization of rough set approximation operation has two major steps, firstly convert the information system from multiple valued one to single valued formal context, secondly realize rough set approximation operations aided by concept lattice, which is equivalent to a query operation under some necessary conditions.

Partitioning of Any Infinite Set with the Aid of Non-Surjective Injective Maps and the Study of a Remarkable Semigroup

In this article, we will present a particularly remarkable partitioning method of any infinite set with the aid of non-surjective injective maps. The non-surjective injective maps from an infinite set to itself constitute a semigroup for the law of composition bundled with certain properties allowing us to prove the existence of remarkable elements. Not to mention a compatible equivalence relation that allows transferring the said law to the quotient set, which can be provided with a lattice structure. Finally, we will present the concept of Co-injectivity and some of its properties.

α-Input and α-Unit Resolution Methods for Generalized Horn Clause Set in L_(V(n×2))F(X)

a-Input resolution and a-unit resolution for generalized Horn clause set are discussed in linguistic truth-valued lattice-valued first-order logic （ Lv（ n × 2） F（X） ）, which can represent and handle uncertain linguistic values-based information. Firstly the concepts of a-input resolution and a.unit resolution are presented, and the equivalence of them is shown. Then α-input （a-unit） resolution is equivalently transformed from Lv（ n × 2） F（X） into that of LnP（X）, and their soundness and completeness are also established. Finally an algorithm for a-unit resolution is contrived in LnP（ X）.

Fuzzy Set Approximations in Fuzzy Formal Contexts

In this paper, a kind of multi-level formal concept is introduced. Based on the proposed multi-level formal concept,we present a pair of rough fuzzy set approximations within fuzzy formal contexts.By the proposed rough fuzzy set approximations,we can approximate a fuzzy set according to different precision level.We discuss the properties of the proposed approximation operators in detail.