A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis

Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.

P-Indeterminate Vector Similarity Measures of Orthopair Neutrosophic Number Sets and Their Decision-MakingMethod with Indeterminate Degrees

In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrates its advantages in the indeterminate information expression,aggregations,and DM problems with some indeterminate ranges.However,the existing research lacks some similarity measures between ONNSs.They are indispensable mathematical tools and play a crucial role in DM,pattern recognition,and clustering analysis.Thus,it is necessary to propose some similaritymeasures betweenONNSs to supplement the gap.To solve the issue,this study firstly proposes the p-indeterminate cosine measure,p-indeterminate Dice measure,p-indeterminate Jaccard measure of ONNSs(i.e.,the three parameterized indeterminate vector similarity measures of ONNSs)in vector space.Then,a DMmethod based on the parameterized indeterminate vector similarity measures of ONNSs is developed to solve indeterminate multiple attribute DM problems by choosing different indeterminate degrees of the parameter p,such as the small indeterminate degree(p=0)or the moderate indeterminate degree(p=0.5)or the big indeterminate degree(p=1).Lastly,an actual DM example on choosing a suitable logistics supplier is provided to demonstrate the flexibility and practicability of the developed DM approach in indeterminate DM problems.By comparison with existing relative DM methods,the superiority of this study is that the established DMapproach indicates its flexibility and suitability depending on decision makers’indeterminate degrees(decision risks)in ONNS setting.

Similarity measure design and similarity computation for discrete fuzzy data

The similarity computations for fuzzy membership function pairs were carried out.Fuzzy number related knowledge was introduced,and conventional similarity was compared with distance based similarity measure.The usefulness of the proposed similarity measure was verified.The results show that the proposed similarity measure could be applied to ordinary fuzzy membership functions,though it was not easy to design.Through conventional results on the calculation of similarity for fuzzy membership pair,fuzzy membership-crisp pair and crisp-crisp pair were carried out.The proposed distance based similarity measure represented rational performance with the heuristic point of view.Furthermore,troublesome in fuzzy number based similarity measure for abnormal universe of discourse case was discussed.Finally,the similarity measure computation for various membership function pairs was discussed with other conventional results.

Similarity measure application to fault detection of flight system

差错察觉技术与类似措施被介绍。常规类似措施的特征基于模糊数字被讨论。在距离措施的帮助下，类似措施明确地被构造。设计基于距离的类似措施对包括非凸的模糊会员功能的一般模糊会员功能适用，而模糊基于数字的类似措施有限制计算一般模糊会员功能的类似。到一般模糊会员结构的建议类似措施的适用性被识别定义证明。为了决定，指责飞行系统的察觉，试验性的数据(投球的时刻系数和电梯系数) 被转变成模糊会员函数。基于距离的类似措施被用于获得的模糊会员功能，和类似计算，分析与差错和正常操作系数被获得。

Similarity solutions of Prandtl mixing length modelled two dimensional turbulent boundary layer equations

The exact similarity solutions of two dimensional laminar boundary layer were obtained by Blasius in 1908,however,for two dimensional turbulent boundary layers,no Blasius type similarity solutions(special exact solutions)have ever been found.In the light of Blasius’pioneer works,we extend Blasius similarity transformation to the two dimensional turbulent boundary layers,and for a special case of flow modelled by Prandtl mixing-length,we successfully transform the two dimensional turbulent boundary layers partial differential equations into a single ordinary differential equation.The ordinary differential equation is numerically solved and some useful quantities are produced.For numerical calculations,a complete Maple code is provided.

Study on the Size Distribution and Similarity Law of Bubble Nuclei in Water

To study the distribution characteristics and similarity laws of nuclei under different pressures,based on the selfdesigned decompression chamber and the acoustic measuring system,the size distributions of nuclei in the degassed tap water under negative ambient pressures were measured.A number density distribution function of nuclei based on the modified Weibull distribution function was proposed and verified by the experimental measurement results and some published data of nuclei size distribution.Based on this nuclei number density distribution function,the similarity law of the nuclei size distribution was analyzed:in the scale experiment,the value of exponential in the similarity law of the nuclei number density should be determined by the nuclei size distribution of the water in the prototype experiment and the actual nuclei size distribution of the water in the model experiment.And a precondition is that the nuclei size distributions are similar.

Dimensional and Mechanical Similarity Analysis of the Flow in Rotating Liquid Film Reactor

A rotating liquid film reactor (RLFR) is a device of two coaxial rotating conical cylinders with the inner cone rotating and the outer one stationary. A complete mathematical model for the flow between the conical cylinders is built and a dimensional analysis is carried out. It is proved that at each point of the flow field the dimensionless pressure and velocity of the flow are determined by parameters: Reynolds number (Re), aspect ratio (Γ), radius ratio (η) and wall inclination angle (α). Furthermore, a sufficient and a necessary condition are derived from mechanical similarity between RLFR and a manufacturing equipment geometrically similar to RLFR. Finally, a numerical simulation for the distribution of pressure and velocity is performed. The results may provide a theoretical basis for experiment method and numerical simulation of the flow in a RLFR-like device.

Hans A.Panofsky’s Integral Similarity Function—At Fifty

Fifty years ago, Hans A. Panofsky published a paper entitled Determination of stress from wind and temperature measurements. In his famous paper, he presented a new profile function for the mean horizontal wind speed under the condition of diabatic stratification that includes his integral similarity function. With his integral similarity function, he opened the door for Monin-Obukhov scaling in a wide range of micrometeorological and microclimatological applications. In a historic survey ranging from the sixties of the past century down to the present days, we present integral similarity functions for momentum, sensible heat, and water vapor for both unstable and stable stratification, where on the one hand free convection condition and on the other hand strongly stable stratification are addressed.

基于直觉模糊环境的海上风机选型

选择合适的海上风力发电机机型对海上风电场的长期高效运行起着至关重要的作用。针对决策者在风机选型决策过程中存在不确定性和主观偏好等问题,提出一种改进的多准则决策(multi-criteria decision making, MCDM)框架及方法:在权重求解算法中将群体决策和直觉模糊数与层次分析法相结合,提出群体直觉模糊层次分析法(group intuitionistic fuzzy analytic hierarchy process, GIAHP)计算指标权重;在备选方案排序算法中将余弦距离引入接近理想点法(technique for order preference by similarity to an ideal solution, TOPSIS),提出多距离TOPSIS确定备选方案排序。最后以山东省海上风电场风机选型为例,并通过敏感性分析验证框架及方法的鲁棒性。该框架及方法为中国海上风电场风机选型提供理论依据,可确保海上风电场长期稳定运行。

基于相似度的三参数区间灰数决策方法

为了解决复杂决策环境中的多属性群决策问题,考虑问题的灰数特质及决策者的心理因素,提出了基于相似度的三参数区间灰数决策方法。首先,从区间长度和重心的角度出发,提出了相似度计算公式。其次,考虑决策者与环境的关系,建立基于相似度的决策者心理认知场,引入数据势理论,求得决策者权重;结合距离公式和熵权法求得属性权重;最后,构建了基于前景理论、相似度和逼近理想解排序法相结合的方案决策模型。采用算例证明了模型具有优化方案之间的差异度的效果,并验证了可操作性及合理性。

多种介质影响下涡街流量计的计量性能比较

涡街流量计是一种常用的流量测量仪表,用于测量液体、气体等流体介质。涡街流量计在不同介质下的计量性能存在差异,这主要是由于流体介质的可压缩性对涡街流量计的影响。通过理论分析和实流标定实验,研究涡街流量计在不同介质下的计量性能。结果表明,介质的可压缩性和涡街流量计的几何尺寸是影响计量性能的重要因素,不同介质下的涡街流量计需要进行修正。这些研究结果对于涡街流量计在实际应用中的准确测量提供了理论依据和实验指导。

Signal processing for real-time identification of similar metals by laser-induced breakdown spectroscopy

Laser-induced breakdown spectroscopy(LIBS) is regarded as a promising technique for realtime sorting of scrap metals due to its capability of fast multi-elemental and in-air analysis. This work reports a method for signal processing which ensures high accuracy and high speed during similar metal sorting by LIBS. Similar metals such as aluminum alloys or stainless steel are characterized by nearly the same constituent elements with slight variations in elemental concentration depending on metal type. In the proposed method, the original data matrix is substantially reduced for fast processing by selecting new input variables(spectral lines) using the information for the constituent elements of similar metals. Specifically, principal component analysis(PCA) of full-spectra LIBS data was performed and then, based on the loading plots, the input variables of greater significance were selected in the order of higher weights for each constituent element. The results for the classification test with aluminum alloy, copper alloy,stainless steel and cast steel showed that the classification accuracy of the proposed method was nearly the same as that of full-spectra PCA, but the computation time was reduced by a factor of 20 or more. The results demonstrated that incorporating the information for constituent elements can significantly accelerate classification speed without loss of accuracy.

区间二型模糊语言Z-numbers及其应用

针对区间二型模糊多属性群决策问题,提出了以区间二型模糊语言Z-numbers(IT2FLZNs)为信息环境的群决策方法。首先,在区间二型模糊集和Z-numbers理论基础上提出了区间二型模糊语言Znumbers并定义了其相关运算性质,提出了两个区间二型模糊语言Z-numbers之间的相似度与距离;其次,在专家和属性权重都未知的情况下,根据决策中总体不确定性最小原则,利用相似度构建最优化模型,确定专家和属性的权重,并且通过综合比较各方案的群体效用值、个体遗憾值和亲密度来选择最优方案;最后,通过一个银行流动风险的实例验证所提方法的有效性与可行性。

Numerical Solution for a Similar Flow between Two Disks in the Presence of a Magnetic Field

Numerical solutions are obtained for non-steady, incompressible fluid flow between two parallel disks which at time t are separated by a distance H(1-αt)1/2 and a magnetic field proportional to B0(1-αt) -1/2 is applied perpendicular to the disks where H denotes a representative length, BO denotes a representative magnetic field and α-1 denotes a representative time. Similarity transformations are used to convert the governing partial differential equations of motion in to ordinary differential form. The resulting ordinary differential equations are solved numerically using SOR method, Richardson extrapolation and Simpson’s (1/3) Rule. Our numerical scheme is straightforward, efficient and easy to program.

Numerical Study on the Relationship between the Number of Ferritin Subunits and the Size of Outer Diameter

Ferritin is assembled from sub-chains into a spherical shape. We have found that the number of sub-chains is generally 3, 6, 8, 12, 24, 36, and the corresponding spherical volume (outer diameter) is also different. In this paper, using the protein structural data from PDB website, linear regression was carried out to model the relationship between sub-chain number and outer diameter of 25 ferritins by calculation and analysis, but the results were not ideal. In order to improve the model, we divided the 25 proteins into two groups by molecular evolution, followed by the establishment of a linear model. The correlation coefficient of one group was R2 = 0.98. Based on calculations and modelling, we hypothesize that the new ferritin formed by the 3kx9 site-directed mutagenesis is no longer 24-chain, but a 36-chain mutant.

DECAY RATE OF FOURIER TRANSFORMS OF SOME SELF-SIMILAR MEASURES

This paper is concerned with the Diophantine properties of the sequence {ξθn}, where 1 ≤ξ 〈 θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μλ with λ = θ-1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μλ ahaost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem.

BERNOULLI CONVOLUTIONS ASSOCIATED WITH CERTAIN NON-PISOT NUMBERS

The Bernoulli convolution ν λ measure is shown to be absolutely continuous with L 2 density for almost all 12<λ<1,and singular if λ -1 is a Pisot number. It is an open question whether the Pisot type Bernoulli convolutions are the only singular ones. In this paper,we construct a family of non-Pisot type Bernoulli convolutions ν λ such that their density functions,if they exist,are not L 2. We also construct other Bernolulli convolutions whose density functions,if they exist,behave rather badly.

Fuzzy cluster analysis of water mass in the western Taiwan Strait in spring 2019

The classification of the springtime water mass has an important influence on the hydrography,regional climate change and fishery in the Taiwan Strait.Based on 58 stations of CTD profiling data collected in the western and southwestern Taiwan Strait during the spring cruise of 2019,we analyze the spatial distributions of temperature(T)and salinity(S)in the investigation area.Then by using the fuzzy cluster method combined with the T-S similarity number,we classify the investigation area into 5 water masses:the Minzhe Coastal Water(MZCW),the Taiwan Strait Mixed Water(TSMW),the South China Sea Surface Water(SCSSW),the South China Sea Subsurface Water(SCSUW)and the Kuroshio Branch Water(KBW).The MZCW appears in the near surface layer along the western coast of Taiwan Strait,showing low-salinity(<32.0)tongues near the Minjiang River Estuary and the Xiamen Bay mouth.The TSMW covers most upper layer of the investigation area.The SCSSW is mainly distributed in the upper layer of the southwestern Taiwan Strait,beneath which is the SCSUW.The KBW is a high temperature(core value of 26.36℃)and high salinity(core value of 34.62)water mass located southeast of the Taiwan Bank and partially in the central Taiwan Strait.

基于高斯混合模型和自适应簇数的文本聚类

针对海量文本难以精准聚类问题,提出了一种基于高斯混合模型和自适应簇数的文本聚类算法(TCA)。首先,采用无意义符号去除、基于齐次马尔科夫假设的文本分词和停用词去除方法,实现数据分词和清洗;其次,提出权衡关键词频率和普适性的关键词权重,选择关键词和进行文本向量化;再次,在高斯混合模型的基础上,引入文本相似度,提出权衡条件概率和相似度的文本权重;最后,通过轮盘赌初始化聚类中心,更新多维高斯分布模型参数,实现分簇数量确定的文本聚类。同时,为了自适应文本分簇数量,在肘部法则的基础上确定最优分簇数量,从而提高聚类效果。仿真结果表明:TCA能自适应文本聚类数量和获得其分布,提高聚类的准确率和召回率,有助于更好地实现海量文本的精确聚类。

The “3 Genomic Numbers” Discovery: How Our Genome Single-Stranded DNA Sequence Is “Self-Designed” as a Numerical Whole

This article proves the existence of a hyper-precise global numerical meta-architecture unifying, structuring, binding and controlling the billion triplet codons constituting the sequence of single-stranded DNA of the entire human genome. Beyond the evolution and erratic mutations like transposons within the genome, it’s as if the memory of a fossil genome with multiple symmetries persists. This recalls the “intermingling” of information characterizing the fractal universe of chaos theory. The result leads to a balanced and perfect tuning between the masses of the two strands of the huge DNA molecule that constitute our genome. We show here how codon populations forming the single-stranded DNA sequences can constitute a critical approach to the understanding of junk DNA function. Then, we suggest revisiting certain methods published in our 2009 book “Codex Biogenesis”. In fact, we demonstrate here how the universal genetic code table is a powerful analytical filter to characterize single-stranded DNA sequences constituting chromosomes and genomes. We can then show that any genomic DNA sequence is featured by three numbers, which characterize it and its 64 codon populations with correlations greater than 99%. The number “1” is common to all sequences, expressing the second law of Chargaff. The other 2 numbers are related to each specific DNA sequence case characterizing life species. For example, the entire human genome is characterized by three remarkable numbers 1, 2, and Phi = 1.618 the golden ratio. Associated with each of these three numbers, we can match three axes of symmetry, then “imagine” a kind of hyperspace formed by these codon populations. Then we revisit the value (3-Phi)/2 which is probably universal and common to both the scale of quarks and atomic levels, balancing and tuning the whole human genome codon population. Finally, we demonstrate a new kind of duality between “form and substance” overlapping the whole human genome: we will show that—simultaneously with the duality between genes and junk DNA—there is a second layer of embedded hidden structure overlapping all the DNA of the whole human genome, dividing it into a second type of duality information/redundancy involving golden ratio proportions.