Legendre-Weighted Residual Methods for System of Fractional Order Differential Equations

The numerical approach for finding the solution of fractional order systems of boundary value problems (BPVs) is derived in this paper. The implementation of the weighted residuals such as Galerkin, Least Square, and Collocation methods are included for solving fractional order differential equations, which is broadened to acquire the approximate solutions of fractional order systems with differentiable polynomials, namely Legendre polynomials, as basis functions. The algorithm of the residual formulations of matrix form can be coded efficiently. The interpretation of Caputo fractional derivatives is employed here. We have demonstrated these methods numerically through a few examples of linear and nonlinear BVPs. The results in absolute errors show that the present method efficiently finds the numerical solutions of fractional order systems of differential equations.

Approach to obtaining weights of uncertain ordered weighted geometric averaging operator

The ordered weighted geometric averaging（OWGA） operator is extended to accommodate uncertain conditions where all input arguments take the forms of interval numbers. First, a possibility degree formula for the comparison between interval numbers is introduced. It is proved that the introduced formula is equivalent to the existing formulae, and also some desired properties of the possibility degree is presented. Secondly, the uncertain OWGA operator is investigated in which the associated weighting parameters cannot be specified, but value ranges can be obtained and the associated aggregated values of an uncertain OWGA operator are known. A linear objective-programming model is established; by solving this model, the associated weights vector of an uncertain OWGA operator can be determined, and also the estimated aggregated values of the alternatives can be obtained. Then the alternatives can be ranked by the comparison of the estimated aggregated values using the possibility degree formula. Finally, a numerical example is given to show the feasibility and effectiveness of the developed method.

Generalized ordered weighted averaging operators based methods for MADM in intuitionistic fuzzy set setting

Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.

Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator

The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.

Influence of birth order, birth weight, colostrum and serum immunoglobulin G on neonatal piglet survival

Background： Intake of colostrum after birth is essential to stimulate intestinal growth and function, and to provide systemic immunological protection via absorption of Immunoglobulin G （IgG）. The birth order and weight of 745 piglets （from 75 litters） were recorded during a one-week period of farrowing. Only pigs weighing greater than 0.68 kg birth weight were chosen for the trial. Sow colostrum was collected during parturition, and piglets were bled between 48 and 72 hours post-birth. Piglet serum IgG and colostral IgG concentrations were determined by radial immunodiffusion. Results： Sow parity had a significant （P 〈 0.001） effect on sow colostral IgG concentration, being 5% higher in multiparous females. Sow colostral IgG concentration explained 6% and piglet birth order accounted for another 4% of the variation observed in piglet serum IgG concentration （P 〈 0.05）; however, birth weight had no detectable effect. Piglet serum IgG concentration had both a linear （P 〈 0.05） and quadratic effect （P 〈 0.05） on % survival. Piglets with 1,000 mg/dl serum IgG or less （n=24） had a 67% survival; whereas, piglets with IgG concentrations between 2250 to 2500 mg/dl （n=247） had a 91% survival. Birth order had no detectable effect on survival, but birth weight had a positive linear effect （P 〈 0.05）. Piglets weighing 0.9 kg （n = 107） at birth had a 68% survival rate, and those weighing 1.6 kg （n = 158） had an 89% survival. Conclusion： We found that the combination of sow colostrum IgG concentration and birth order can account for 10% of the variation of piglet serum IgG concentration and that piglets with less than 1,000 mg/dl IgG serum concentration and weight of 0.9 kg at birth had low survival rate when compared to their larger siblings. The effective management of colostrum uptake in neonatal piglets in the first 24 hrs post-birth may potentially improve survival from birth to weaning.

Sustainability Intelligent Evaluation of Regional Microgrid Interconnection System Based on Combination Entropy Weight Rank Order-TOPSIS and NILA-KELM

Sustainability evaluation of regional microgrid interconnection system is conducive to a profound and comprehensive understanding of the impact of interconnection system projects.In order to realize the comprehensive and scientific intelligent evaluation of the system,this paper proposes an evaluation model based on combination entropy weight rank order-technique for order preference by similarity to an ideal solution(TOPSIS)and Niche Immune Lion Algorithm-Extreme Learning Machine with Kernel(NILAKELM).Firstly,the sustainability evaluation indicator system of the regional microgrid interconnection system is constructed fromfour aspects of economic,environmental,social,and technical characteristics,and the evaluation indicators are explained.Then,the classical evaluationmodel based on TOPSIS is constructed,and the entropy weight method and rank order method(RO)are coupled to obtain the indicator weight.The niche immune algorithm is used to improve the lion algorithm,and the improved lion algorithm is used to optimize the parameters of KELM,and the intelligent evaluation model based on NILA-KELM is obtained to realize fast real-time calculation.Finally,the scientificity and accuracy of themodel proposed in this paper are verified.The model proposed in this paper has the lowest RMSE,MAE and RE values,indicating that its intelligent evaluation results are the most accurate.This study is conducive to the horizontal comparison of the overall performance of regional microgrid interconnection system projects,helps investors to choose the most promising project scheme,and helps the government to find feasible project.

RESEARCHES ON INVERSE ORDER RULE FOR WEIGHTED GENERALIZED INVERSE

The weighted generalized inverses have several important applications in researching the singular matrices,regularization methods for ill-posed problems, optimization problems and statis- tics problems.In this paper we further research inverse order rules of weighted generalizde inverse. From the view point of munerical algebra, the different methods we used in inverse order rules pro- vide beneficial means for theory and computing of generalized inverse matrices.

Three methods for generating monotonic OWA operator weights with given orness level

Based on the properties of ordered weighted averaging (OWA) operator and regular increasing monotone (RIM) quantifier, three methods for generating monotonic OWA operator weights are proposed. They are geometric OWA operator weights, equidifferent OWA operator weights and the modified RIM quantifier OWA weights. Compared with most of the common OWA methods for generating weights, the methods proposed in this paper are more intuitive and efficient in computation. And as there are more than one solution in most cases, the decision maker can set some initial condition and chooses the appropriate solution in the real decision process, which increases the flexibility of decision making to some extent. All these three OWA methods for generating weights are illustrated by numerical examples.

Some OWA operator weights determination methods with RIM quantifier

Based on the quantifier guided method,an ordered weighted averaging(OWA)weights generating method under given orness level with regular increasing monotone(RIM)quantifiers is proposed.Then the RIM quantifier based OWA weights generating method is modified to make the generated weights be monotonic,which can be used to express the decision maker's consistent preference information.Finally,both of these weights generating methods are extended to their generic forms,so that they can generate the OWA weights for any ordinary elements set with any given aggregated value.

New HB-weighted time delay estimation algorithm under impulsive noise environment

The traditional HB-weighted time-delay estimation （TDE） method degenerates under the impulsive noise environment. Two new time-delay estimation methods are proposed based on fractional lower order statistics （FLOS） according to the impulsive characteristics of fractional lower order α-stable noises. Theoretic analysis and computer simulations indicate that the proposed covariation based HB weighted （COV-HB） algorithm can suppress impulsive noises in one received signal for 1 ≤α≤ 2, whereas the other proposed fractional lower order eovariancebased HB weighted （FLOC-HB） algorithm has robust performance under arbitrary impulsive noise conditions for the whole range of 0 〈α≤ 2.

Monocular depth ordering with occlusion edges extraction and local depth inference

In this paper, a method to infer global depth ordering for monocular images is presented. Firstly a distance metric is defined with color, compactness, entropy and edge features to estimate the difference between pixels and seeds, which can ensure the superpixels to obtain more accurate object contours. To correctly infer local depth relationship, a weighting descriptor is designed that combines edge, T-junction and saliency features to avoid wrong local inference caused by a single feature. Based on the weighting descriptor, a global inference strategy is presented,which not only can promote the performance of global depth ordering, but also can infer the depth relationships correctly between two non-adjacent regions. The simulation results on the BSDS500 dataset, Cornell dataset and NYU 2 dataset demonstrate the effectiveness of the approach.

IMPROVEMENT AND REALIZATION FOR THE MAXIMUM WEIGHT MATCHING ALGORITHM

Some new concepts of effective incidence matrix,ascending order adjacency matrix andend-result vertex are introduced,and some improvements of the maximum weight matchingalgorithm are made.With this method a computer program in FORTRAN language is realized onthe computers FELIX C-512 and IBM-PC.Good results are obtained in practical operations.

WEIGHTED COMPACT SCHEME FOR SHOCK CAPTURING

A new class of finite difference schemes--the weighted compact schemes are proposed. According to the idea of the WENO schemes, the weighted compact scheme is constructed by a combination of the approximations of derivatives on candidate stencils with properly assigned weights so that the non oscillatory property is achieved when discontinuities appear. The primitive function reconstruction method of ENO schemes is applied to obtain the conservative form of the weighted compact scheme. This new scheme not only preserves the characteristic of standard compact schemes and achieves high order accuracy and high resolution using a compact stencil, but also can accurately capture shock waves and discontinuities without oscillation. Numerical examples show that the new scheme is very promising and successful.

Weighted Self-Adaptive Threshold Wavelets for Interpolation Point Selection Used in Interconnect MOR

As process technology development,model order reduction( MOR) has been regarded as a useful tool in analysis of on-chip interconnects. We propose a weighted self-adaptive threshold wavelet interpolation MOR method on account of Krylov subspace techniques. The interpolation points are selected by Haar wavelet using weighted self-adaptive threshold methods dynamically. Through the analyses of different types of circuits in very large scale integration( VLSI),the results show that the method proposed in this paper can be more accurate and efficient than Krylov subspace method of multi-shift expansion point using Haar wavelet that are no weighted self-adaptive threshold application in interest frequency range,and more accurate than Krylov subspace method of multi-shift expansion point based on the uniform interpolation point.

高阶精度非线性加权格式权函数研究综述

在简述用于捕捉间断的非线性格式发展历程的基础上,依托五阶精度WENO格式,介绍了非线性加权格式在候选模板集选取、光滑度指标计算方法及其与非线性权的函数关系等方面做出的努力。对于非等宽候选模板集的情况,给出了保证非线性加权格式精度的非线性权的量阶关系,强调了光滑度指标计算方法对格式精度和效率的重要性,提出了进一步开展多宽度模板集非线性加权格式研究的建议。

WFRFT modulation recognition based on HOC and optimal order searching algorithm

A hybrid carrier（HC） scheme based on weighted-type fractional Fourier transform（WFRFT） has been proposed recently.While most of the works focus on HC scheme＇s inherent characteristics, little attention is paid to the WFRFT modulation recognition.In this paper, a new theory is provided to recognize the WFRFT modulation based on higher order cumulants（HOC）. First, it is deduced that the optimal WFRFT received order can be obtained through the minimization of 4 th-order cumulants, C_（42）. Then, a combinatorial searching algorithm is designed to minimize C_（42）.Finally, simulation results show that the designed scheme has a high recognition rate and the combinatorial searching algorithm is effective and reliable.

基于有序加权平均算子和后悔理论的城市洪涝灾害韧性评价

针对城市洪涝灾害韧性评价过程主观性强、未考虑决策者有限理性和后悔规避的心理行为导致评价结果失真的难题,提出基于有序加权平均算子和后悔理论的城市洪涝灾害韧性评价方法。首先,结合韧性城市概念,从抵抗能力、预警能力、适应能力、恢复能力4个维度构建指标体系,利用有序加权平均算子将专家极端决策值分布到权重较低位置,通过组合权重的形式求得指标权重,弱化主观偏好极端评价值对权重的影响;然后,考虑专家决策时后悔心理行为特征,构建效用值矩阵、后悔-欣喜值矩阵和感知效用矩阵,得出城市洪涝灾害韧性评价值;最后,将其运用在河南省洪涝灾害韧性评价中,并将计算结果与其他评价方法得出的结果对比分析。结果表明:4种方法评价结果基本一致,均认为河南省洪涝灾害韧性等级为Ⅲ级,提出的方法评价结果精度更高、更贴近实际情况。此外,各地级市韧性等级差异较大,分布不均,整体呈现西南部城市韧性等级高于东北部城市的特征。

A Novel Symbolic Algorithm for Maximum Weighted Matching in Bipartite Graphs

The maximum weighted matching problem in bipartite graphs is one of the classic combinatorial optimization problems, and arises in many different applications. Ordered binary decision diagram (OBDD) or algebraic decision diagram (ADD) or variants thereof provides canonical forms to represent and manipulate Boolean functions and pseudo-Boolean functions efficiently. ADD and OBDD-based symbolic algorithms give improved results for large-scale combinatorial optimization problems by searching nodes and edges implicitly. We present novel symbolic ADD formulation and algorithm for maximum weighted matching in bipartite graphs. The symbolic algorithm implements the Hungarian algorithm in the context of ADD and OBDD formulation and manipulations. It begins by setting feasible labelings of nodes and then iterates through a sequence of phases. Each phase is divided into two stages. The first stage is building equality bipartite graphs, and the second one is finding maximum cardinality matching in equality bipartite graph. The second stage iterates through the following steps: greedily searching initial matching, building layered network, backward traversing node-disjoint augmenting paths, updating cardinality matching and building residual network. The symbolic algorithm does not require explicit enumeration of the nodes and edges, and therefore can handle many complex executions in each step. Simulation experiments indicate that symbolic algorithm is competitive with traditional algorithms.

基于加权逼近理想解排序法对儿科应用喜炎平注射液的药物利用评价

目的:探讨喜炎平注射液药物利用评价(DUE)标准的建立与应用,为喜炎平注射液在儿童患者中的合理使用提供参考。方法:以喜炎平注射液说明书为基础,参考相关共识及指南建立新乡市第一人民医院喜炎平注射液DUE标准,并采用加权逼近理想解排序(TOPSIS)法对我院2023年3-6月使用喜炎平注射液的130份患儿归档病历进行评价及分析。结果:制订的喜炎平注射液DUE标准包括用药指征、用药过程、用药结果3个方面,11项评价指标。经评价我医院患儿在喜炎平注射液使用过程中存在的主要问题为用法用量不适宜24例(18.46%)、无适应证用药15例(11.54%)、用药疗程不适宜12例(9.23%)、给药速度不适宜6例(4.62%)。结论:基于加权TOPSIS法的儿科应用喜炎平注射液DUE方法可综合多个评价指标,操作性强,评价方法简便灵活,但我院儿科喜炎平注射液的临床应用存在不合理使用现象,应加强点评和干预。

基于博弈论组合赋权-云模型的消防员训练损伤风险评估

为降低消防员训练损伤发生率,从个人因素、环境因素和组织管理因素3个方面,提出包含19个指标的消防员训练损伤风险评估指标体系;采用Bonferroni有序加权平均算子(BON-OWA算子)修正层次分析法(AHP)的误差,获得各指标的主观权重;引用基于指标相关性的权重确定法(CRITIC)确定各指标的客观权重;基于博弈论组合赋权法确定各指标的组合权重;引入云模型理论,建立消防员训练损伤风险评估模型,并以河南省某消防救援大队消防员的训练为例,验证该模型的科学性。结果表明:训练装备的战技性能状况指标对消防员的训练损伤风险等级影响最大;该风险评估模型通过数据处理,可以确定消防员训练损伤风险等级;案例中,消防员在5种不同情景下的训练损伤风险等级均为一般风险,这与模糊综合评价法所得结果一致。