基于模糊判断矩阵信息确定专家权重的方法

本文对群组模糊判断矩阵集结过程中确定专家权重的问题进行了研究,建立了模糊判断矩阵的特征矩阵和求解群集结矩阵的最优化模型,通过矩阵之间距离度量判断信息自身逻辑一致性程度和群体相容性程度,给出一种基于专家判断信息的可信度计算其后验权重的方法,最后用算例予以说明.     

ASSESSING ENVIRONMENTAL SCANNING AT THE SUBUNIT LEVEL: A MULTITRAIT-MULTIMETHOD ANALYSIS*

Environmental scanning activities of over 400 top management subunits in 108 European manufacturing firms provided the data base for this research. Four traits (constructs) of scanning using three methods (interest, frequency, and time) were examined. A confirmatory factor analysis approach to multitrait-multimethod (MTMM) data was employed. Verification of the reliability as well as convergent and discriminant validity of the scanning scales are reported and discussed. The viability of confirmatory factor analysis in providing a precise analysis of partitioning variance according to trait, method, and error is demonstrated.     

Graph colouring approach for cell formation problems

This paper presents a graph-theoretic approach for solving the clustering problem in group technology. The machine-component incidence matrix is used to form the weight matrix. Using the two weight matrices, one for the machines and the other for the parts, two graphs are developed. The nodes of each graph are coloured using the proper colouring method. An edge, whose adjacent nodes are of same colour, partitions the graph into subgraphs, thus creating machine-part cells. This cell formation method yields solutions which compare favourably with respect to other available methods. This procedure is illustrated using an example problem from the literature.     

Benders decomposition for set covering problems

This paper describes Benders decomposition approaches to optimally solve set covering problems “ almost” satisfying the consecutive ones property. The decompositions are based on the fact that set covering problems with consecutive ones property have totally unimodular coefficient matrices. Given a binary matrix, a totally unimodular matrix is enforced by filling up every row with ones between its first and its last non-zero entries. The resulting mistake is handled by introducing additional integer variables whose number depends on the reordering of the columns of the given matrix. This leads us to consider the consecutive block minimization problem. Two cutting plane algorithms are proposed and run on a large set of benchmark instances. The results obtained show that the cutting plane algorithms outperform an existing tree search method designed exclusively for such instances.     

The Steiner Tree Problem in Kalmanson Matrices and in Circulant Matrices

We investigate the computational complexity of two special cases of the Steiner tree problem where the distance matrix is a Kalmanson matrix or a circulant matrix, respectively. For Kalmanson matrices we develop an efficient polynomial time algorithm that is based on dynamic programming. For circulant matrices we give an -hardness proof and thus establish computational intractability.     

投入产出分析的几种系数矩阵在管理和经济分析中的作用

综合评价投入产出分析的几种系数矩阵在经济指标分析、经济效益分析和经济预测中的作用。提出投资系数矩阵的近似构造法,改进了利润作为目标函数的优化模型和推广了数学增量模型,并通过矩阵变换法从一个投入产出分析系数矩阵生成另一个相似的投入产出分析系数矩阵。     

Is there potential in assessing for high-potential? Evaluating the relationships between performance ratings,leadership assessment data,designated high-potential status and promotion outcomes in a global organization

While leadership is a critical component of organizational success, organizations need to be more effective at classifying talent based on future potential vs current performance. This need raises the question as to whether the assessment of leadership potential is truly adding value or enhancing the talent review and classification process. Data from 9,784 participants in PepsiCo’s Leadership Assessment and Development (LeAD) program—a multi-trait, multi-method (MTMM) assessment and development process—are used to examine relationships between individual performance, assessed potential, organizationally designated potential, and promotion rates post assessment. Results from the analyses indicate that assessed potential provides unique variance above performance alone in determining process outcomes (i.e., designated potential and promotions), and therefore can be useful for making more informed talent management decisions. The applications of these measures within the current organization as well as limitations of the study and areas for future research are discussed.     

Application of the Fuzzy Weighted Average in Strategic Portfolio Management*

We propose a systematic approach that incorporates fuzzy set theory in conjunction with portfolio matrices to assist managers in reaching a better understanding of the overall competitiveness of their business portfolios. Integer linear programming is also accommodated in the proposed integrated approach to help select strategic plans by using the results derived from the previous portfolio analysis and other financial data. The proposed integrated approach is designed from a strategy‐oriented perspective for portfolio management at the corporate level. It has the advantage of dealing with the uncertainty problem of decision makers in doing evaluation, providing a technique that presents the diversity of confidence and optimism levels of decision makers. Furthermore, integer linear programming is used because it offers an effective quantitative method for managers to allocate constrained resources optimally among proposed strategies. An illustration from a real‐world situation demonstrates the integrated approach. Although a particular portfolio matrix model has been adopted in our research, the procedure proposed here can be modified to incorporate other portfolio matrices.     

Assessment of Uncertainty in High Frequency Data: The Observed Asymptotic Variance

The availability of high frequency financial data has generated a series of estimators based on intra‐day data, improving the quality of large areas of financial econometrics. However, estimating the standard error of these estimators is often challenging. The root of the problem is that traditionally, standard errors rely on estimating a theoretically derived asymptotic variance, and often this asymptotic variance involves substantially more complex quantities than the original parameter to be estimated. Standard errors are important: they are used to assess the precision of estimators in the form of confidence intervals, to create “feasible statistics” for testing, to build forecasting models based on, say, daily estimates, and also to optimize the tuning parameters. The contribution of this paper is to provide an alternative and general solution to this problem, which we call Observed Asymptotic Variance. It is a general nonparametric method for assessing asymptotic variance (AVAR). It provides consistent estimators of AVAR for a broad class of integrated parameters Θ = ∫ θ_t dt, where the spot parameter process θ can be a general semimartingale, with continuous and jump components. The observed AVAR is implemented with the help of a two‐scales method. Its construction works well in the presence of microstructure noise, and when the observation times are irregular or asynchronous in the multivariate case. The methodology is valid for a wide variety of estimators, including the standard ones for variance and covariance, and also for more complex estimators, such as, of leverage effects, high frequency betas, and semivariance.     

多性质多目标模糊指派模型在市政工程开发商选择中的应用

考虑了指派问题中涉及到多个目标要求的情况,包括定量目标和定性目标。首先,使用模糊数学的方法将定量目标下的效率值矩阵转化为优选决策矩阵,同时提出了定性目标的量化方法,并建立了定性目标的优选决策矩阵。然后,将各个目标要求下的优选决策矩阵进行了合成,考虑了综合效益对于“优”和“劣”之间多个等级的相对隶属度,建立了多性质、多目标模糊数学模型,得到了分级特征值矩阵。最后,与传统指派模型相结合形成了多性质、多目标模糊指派数学模型,使用匈牙利算法对该模型进行了求解,并结合市政工程在开发商之间分配的例子进行了分析说明。     

基于证据推理的不确定多属性决策方法

针对基本属性权重的不确定性,以及基本属性与广义属性评价集的不一致性等问题,提出一种基于证据推理的不确定多属性决策方法,将证据推理算法推广到更一般的决策环境中.根据决策矩阵的信息熵客观地获得属性的权系数;而对于基本属性与广义属性评价集不一致的情况,则通过对基本属性分布评价的模糊化及模糊变换,合理地实现到广义分布评价的统一形式;最后应用证据推理算法得到整个方案集的排序.实例结果表明,该方法是可行的、有效的.     

Simulation investigation of the stochastic behaviour of selected group technology similarity coefficients

Abstract

Abstract. The problem of restructuring manufacturing facilities into a cellular format has been addressed using a variety of approaches, including block-diagonalization of the machine-component matrix, mathematical programming formulations and cluster analyses. This paper addresses the problem of assessing whether or not the machine-component mix of a particular facility is amenable to cellular restructuring. The focus is cluster analytic; specifically a number of recently developed similarity coefficients are applied to problems generated via Monte Carlo simulation. The results show that, in a number of cases, the quality of the original block diagonal structure had a significant effect on the shape (in particular, skewncss and kurtosis) of the distribution of similarity coefficient values.     

A fast greedy sequential heuristic for the vertex colouring problem based on bitwise operations

In this paper a fast greedy sequential heuristic for the vertex colouring problem is presented. The suggested algorithm builds the same colouring of the graph as the well-known greedy sequential heuristic in which on every step the current vertex is coloured in the minimum possible colour. Our main contributions include introduction of a special matrix of forbidden colours and application of efficient bitwise operations on bit representations of the adjacency and forbidden colours matrices. Computational experiments show that in comparison with the classical greedy heuristic the average speedup of the developed approach is 2.6 times on DIMACS instances.     

基于贝叶斯Wishart波动模型的原油市场与股市动态相依性研究

针对时变相关系数矩阵在多变量随机波动模型的估计问题,构建了贝叶斯动态相关Wishart波动模型。在CC-MSV模型的基础上,设置精度矩阵服从Wishart分布,使得模型的相关系数矩阵具有时变特征。通过模型的统计结构分析,选择参数先验分布,设计相应的Gibbs-MTM-ARMS混合算法,据此估计模型参数;并利用上证综合指数、标普500指数与原油期货价格数据进行实证分析。研究结果表明：模型能够有效地刻画原油市场与股票市场的动态相依性;金融危机期间,股票市场与原油市场的相关性较强,并且难以判断正负方向;金融危机后,中国股票市场与原油市场呈现极微弱的相关性,而美国股票市场与原油市场的正相关性较为明显。     

How to Design Rating Schemes of Risk Matrices: A Sequential Updating Approach

Risk matrices have been widely used as a risk evaluation tool in many fields due to their simplicity and intuitive nature. Designing a rating scheme, i.e., determining the number of ratings used in a risk matrix and assigning different ratings to different cells, is an essential part of risk matrix construction. However, most of the related literature has focused on applying a risk matrix to various fields, instead of researching how to design risk matrices. Based on the analysis of several current rules, we propose a new approach, namely, the sequential updating approach (SUA), to design the rating scheme of a risk matrix in a reliable way. In this article, we propose three principles and a rating algorithm based on these principles. The three principles, namely, adjusted weak consistency, consistent internality, and continuous screening, characterize a good rating scheme. The resulting rating scheme has been proven to be unique. A global rating algorithm is then proposed to create the design that satisfies the three principles. We then explore the performance of the SUA. An illustrative application is first given to explain the feasibility of our approach. The sensitivity analysis shows that our method captures a resolution‐reliability tradeoff for decisionmakers in choosing an appropriate rating scheme for a risk matrix. Finally, we compare the designs based on the SUA and Cox's axioms, highlighting the advantages of the SUA.     

群组决策中三角模糊数互补判断矩阵的相容性及方案排序研究

针对专家偏好信息为三角模糊数互补判断矩阵的群组决策问题,研究偏好信息的相容性及方案排序问题。基于Hamming 距离的概念,首先给出了衡量两个三角模糊数相容性的一个指标,并研究了该指标的相关性质;其次,根据三角模糊数互补判断矩阵的特点,给出了三角模糊数互补判断矩阵的相容性指标;以相容性指标为依据设定专家权重,进而给出了一种方案排序方法。最后,算例验证了方法的有效性。     

The bandpass problem: combinatorial optimization and library of problems

A combinatorial optimization problem, called the Bandpass Problem, is introduced. Given a rectangular matrix A of binary elements {0,1} and a positive integer B called the Bandpass Number, a set of B consecutive non-zero elements in any column is called a Bandpass. No two bandpasses in the same column can have common rows. The Bandpass problem consists of finding an optimal permutation of rows of the matrix, which produces the maximum total number of bandpasses having the same given bandpass number in all columns. This combinatorial problem arises in considering the optimal packing of information flows on different wavelengths into groups to obtain the highest available cost reduction in design and operating the optical communication networks using wavelength division multiplexing technology. Integer programming models of two versions of the bandpass problems are developed. For a matrix A with three or more columns the Bandpass problem is proved to be NP-hard. For matrices with two or one column a polynomial algorithm solving the problem to optimality is presented. For the general case fast performing heuristic polynomial algorithms are presented, which provide near optimal solutions, acceptable for applications. High quality of the generated heuristic solutions has been confirmed in the extensive computational experiments. As an NP-hard combinatorial optimization problem with important applications the Bandpass problem offers a challenge for researchers to develop efficient computational solution methods. To encourage the further research a Library of Bandpass Problems has been developed. The Library is open to public and consists of 90 problems of different sizes (numbers of rows, columns and density of non-zero elements of matrix A and bandpass number B), half of them with known optimal solutions and the second half, without.     

Competent genetic algorithms for weighing matrices

In this paper, we demonstrate that the search for weighing matrices constructed from two circulants can be viewed as a minimization problem together with two competent genetic algorithms to locate optima of an objective function. The motivation to deal with the messy genetic algorithm (mGA) is given from the pioneering results of Goldberg, regarding the ability of the mGA to put tight genes together in a solution which points directly to structural patterns in weighing matrices. In order to take into advantage certain properties of two ternary sequences with zero autocorrelation we use an adaptation of the fast messy GA (fmGA) where we combine mGA with advanced techniques, such as thresholding and tie-breaking. This transformation of the weighing matrices problem to an instance of a combinatorial optimization problem seems to be promising, since we resolved two open cases for weighing matrices as these are listed in the second edition of the Handbook of Combinatorial Designs.     

Deterministic construction of compressed sensing matrices based on semilattices

A central problem in compressed sensing is the construction of sensing matrices. In this paper, we show how to construct sensing matrices by using semilattices, and give many examples of sensing matrices constructed from specific semilattices. Moreover, we show that the new construction for some examples with small parameters gives better sensing matrices compared with previously known constructions.     

A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelation. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas–Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices of circulant type, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a CW(126, 64) and a CW(198, 100), whose existence was previously marked as unresolved in the most recent version of Strassler’s table.