全对策的边际贡献值

全对策是定义在局中人集合的所有分划集上的一类特殊合作对策.本文在效用可转移情形下研究全对策的"值"问题.定义了全对策的边际贡献值,得出全对策的Shapley值,以及具有某些性质的值是边际贡献值,并给出两种边际贡献值的具体表达式,及其一些性质.     

A class of estimators with estimated optimum values in sample surveys

Srivastava and Jhajj (1981) proposed a class of estimators for population mean of a character using auxiliary information and optimum values involving unknown parameters. From the practical point of view, their results have very little utility. In view of practical utility, we propose a class of estimators with estimated optimum values. Further, it is shown that the proposed class with estimated optimum values attains the same minimum mean square error of the class of estimators based on optimum values.     

Records from reversed generalized logistic distribution and associated inference

This paper deals with, the record values from Reversed Generalized Logistic Distribution (RGLD) and the explicit expressions for its means, variances and covariances. Some recurrence relations satisfied by the single and product moments of record values from RGLD are obtained. These recurrence relations will enable one to obtain all the single and product moments of all record values in a simple recursive manner. The limit distribution for record values from RGLD and the entropy of record values from RGLD are investigated. Some associated inference are developed. Finally, we derived example to illustrate our aim.     

扩散方程一种无条件稳定的保正并行有限差分方法

本文针对扩散方程提出了一种保正的并行差分格式,并且这个格式为无条件稳定的.我们在每个时间层将计算区域分成许多个子区域以便于实施并行计算.格式构造中首先我们使用前两个时间层的计算结果在分区界面处通过一种非线性的保正外插来预估子区域界面值.然后在每个子区域内部使用经典的全隐格式进行计算.最后在界面处使用全隐格式进行校正（本质上这一步计算是显式计算）.我们给出了一维与二维情形下的保正并行差分格式,并相应的给出了无条件稳定性证明.数值实验显示此并行格式具有二阶数值精度,而且无条件稳定性与保正性也均在数值实验中得到验证.     

一种考虑决策者风险偏好的区间数多属性决策方法

针对属性值以区间数形式给出的多属性决策问题,提出了一种决策分析方法。在本文中,首先描述了属性值为区间数形式的多属性决策问题;然后通过引入决策者的风险偏好因子将区间数决策信息映射为实数值决策信息,并依据属性值与属性均值绝对偏差的大小确定了属性的权重,在此基础上依据所得权重给出了基于加权和法的方案排序方法,通过对风险偏好因子的不同取值还可进行方案排序的灵敏度分析。最后,通过一个算例说明了本文给出方法的可行性和有效性。     

A stochastic method for robustness analysis in sorting problems

ELECTRE TRI is a multiple criteria decision aiding sorting method with a history of successful real-life applications. In ELECTRE TRI, values for certain parameters have to be provided. We propose a new method, SMAA-TRI, that is based on stochastic multicriteria acceptability analysis (SMAA), for analyzing the stability of such parameters. The stability analysis can be used for deriving robust conclusions. SMAA-TRI allows ELECTRE TRI to be used with uncertain, arbitrarily distributed values for weights, the lambda cutting level, and profiles. The method consists of analyzing finite spaces of arbitrarily distributed parameter values. Monte Carlo simulation is applied in this in order to describe for each alternative the share of parameter values that have it assigned to different categories. We show the real-life applicability by re-analyzing a case study in the field of risk assessment.     

Estimating Missing Values Using Neural Networks

The problem of missing values is common in statistical analysis. One approach to deal with missing values is to delete the incomplete cases from the data set. This approach may disregard valuable information, especially in small samples. An alternative approach is to reconstruct the missing values using the information in the data set. The major purpose of this paper is to investigate how a neural network approach performs compared to statistical techniques for reconstructing missing values. The backpropagation algorithm is used as the learning method to reconstruct missing values. The results of back-propagation are compared with results from two methods, viz., (1) using averages, and (2) using iterative regression analysis, to compute missing values. Experimental results show that backpropagation consistently outperforms other methods in both the training and the test data sets, and suggest that the neural network approach is a useful tool for reconstructing missing values in multivariate analysis.     

不完备信息下的灰色粗糙集成决策模型侯亚林

In this paper, for multiple attribute decision-making problem in which attribute values are interval grey numbers and some of them are null values, a decision model based on grey rough sets integration with incomplete information is proposed. We put forward incidence degree coefficient formula for grey interval, by information entropy theory and analysis technique, the method and principle is presented to fill up null values. We also establish the method of grey interval incidence cluster. Because grey system theory and Rough set theory are complementary each other, decision table with preference information is obtained by the result of grey incidence cluster. An algorithm for inducing decision rules based on rough set theory and the dominance relationship is presented. In some extent, this algorithm can deal with decision-making problem in which the attribute values are interval grey numbers and some of them are null values. Contrasted with classical model of cluster decision-making, the algorithm has an advantage of flexibility and compatibility to new information.     

Two-step coalition values for multichoice games

We introduce and compare several coalition values for multichoice games. Albizuri defined coalition structures and an extension of the Owen coalition value for multichoice games using the average marginal contribution of a player over a set of orderings of the player’s representatives. Following an approach used for cooperative games, we introduce a set of nested or two-step coalition values on multichoice games which measure the value of each coalition and then divide this among the players in the coalition using either a Shapley or Banzhaf value at each step. We show that when a Shapley value is used in both steps, the resulting coalition value coincides with that of Albizuri. We axiomatize the three new coalition values and show that each set of axioms, including that of Albizuri, is independent. Further we show how the multilinear extension can be used to compute the coalition values. We conclude with a brief discussion about the applicability of the different values.     

Weighted Shapley hierarchy levels values

A new class of values for cooperative games with level structure is introduced. We apply a multi-step proceeding to the weighted Shapley values. For characterization, two well-known axiomatizations of the weighted Shapley values are extended, the first one by efficiency and weighted balanced contributions and the second one by weighted standardness for two-player games and consistency. We get a new axiomatization of the Shapley levels value too.     

Improving demand forecasting accuracy using nonlinear programming software

We address the problem of forecasting real time series with a proportion of zero values and a great variability among the nonzero values. In order to calculate forecasts for a time series, the model coefficients must be estimated. The appropriate choice of values for the smoothing parameters in exponential smoothing methods relies on the minimization of the fitting errors of historical data. We adapt the generalized Holt–Winters formulation so that it can consider the starting values of the local components of level, trend and seasonality as decision variables of the nonlinear programming problem associated with this forecasting procedure. A spreadsheet model is used to solve the problems of optimization efficiently. We show that our approach produces accurate forecasts with little data per product.     

Mixed Norm Inequalities for Directional Operators Associated to Potentials

We study mixed norm inequalities for directional operators which appear applying the method of rotations to homogeneous operators with variable kernel and with the homogeneity of Riesz potentials. The results are sharp for a range of values of the parameter and for all its values when the inequalities are restricted to radial functions.     

Extreme determinants on the convex hull of matrices with prescribed singular values

In a recent paper[1] the author carried through a comprehesive analysis of the diagonal elements of matrices having prescribed singular values, and as an application of this analysis a characterization was obtained of matrices with prescribed singular values. In the present note we obtain the greatest and least values for the determinants of the matrices in such convex hulls.     

Relations for multiple zeta values

We prove new relations for multiple zeta values. In particular, they imply Vasil’ev’s equality and a formula for the summation of multiple zeta values of fixed weight with a constraint on the first coordinate.     

Anamorphoses and Flat Morphological Operators on Power Lattices

Flat morphological operators are operators on grey-level images derived from increasing set operators by a combination of thresholding and stacking. For analog grey-levels, they commute with anamorphoses or contrast mappings, that is, continuous increasing grey-level transformations; when the underlying set operator is upper semi-continuous, they also commute with thresholding. For bounded discrete grey-levels, commutation with increasing grey-level transformations and with thresholding is guaranteed, without any continuity conditions. In this paper we consider flat operators for images defined on an arbitrary space of points and taking their values in an arbitrary complete lattice. We study their commutation with increasing transformations of values. This requires some continuity requirements on the transformations of values or on the underlying set operator, which are expressed in terms of the lattice of values. We obtain as particular cases the known conditions for analog and discrete grey-levels, and also new conditions for other examples of values: multivalued vectors or any finite set of values.     

Indexing Distributions of Data: Preservice Teachers' Notions of Representativeness

The purpose of the study was to identify strategies used by preservice elementary teachers to index distributions of data. A secondary purpose of the study was to investigate whether representational form influenced the type of representative values constructed. Two hundred eighty‐three preservice teachers were administered a selection of tasks requiring them to construct representative values for a variety of distributional shapes. Participants were asked to provide justifications for their chosen representative measures. Data were analyzed from two perspectives: nature and adequacy of representative measure. Results indicated that when presented with skewed data sets, over half of the participants constructed poorly representative values. Symmetric data sets were best indexed with 67% of participants constructing highly representative values. Representational form played a significant role in determining representative values. Data presented graphically were more likely to be represented using measures of variability than were those presented nongraphically. Conversely, measures of central tendency were more frequently used to represent nongraphical data. The information arising from this study indicates that many preservice teachers construct poorly representative values to index data sets and utilize identical measures of representativeness regardless of distributional shape. The findings of the study highlight the need for exploratory data activities at the preservice level, call for provision of experiences affording insights into construction of representative values, and thus, have implications for the design of preservice mathematics education curricula.     

An efficient algorithm for mining high utility itemsets with negative item values in large databases

Utility itemsets typically consist of items with different values such as utilities, and the aim of utility mining is to identify the itemsets with highest utilities. In the past studies on utility mining, the values of utility itemsets were considered as positive. In some applications, however, an itemset may be associated with negative item values. Hence, discovery of high utility itemsets with negative item values is important for mining interesting patterns like association rules. In this paper, we propose a novel method, namely HUINIV (High Utility Itemsets with Negative Item Values)-Mine, for efficiently and effectively mining high utility itemsets from large databases with consideration of negative item values. To the best of our knowledge, this is the first work that considers the concept of negative item values in utility mining. The novel contribution of HUINIV-Mine is that it can effectively identify high utility itemsets by generating fewer high transaction-weighted utilization itemsets such that the execution time can be reduced substantially in mining the high utility itemsets. In this way, the process of discovering all high utility itemsets with consideration of negative item values can be accomplished effectively with less requirements on memory space and CPU I/O. This meets the critical requirements of temporal and spatial efficiency for mining high utility itemsets with negative item values. Through experimental evaluation, it is shown that HUINIV-Mine outperforms other methods substantially by generating much less candidate itemsets under different experimental conditions.     

Computation of continuous and piecewise affine Lyapunov functions for discrete-time systems

In this paper, we present a new approach for computing Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. Given a suitable triangulation of a compact neighbourhood of the origin, a continuous and piecewise affine function can be parameterized by the values at the vertices of the triangulation. If these vertex values satisfy system-dependent linear inequalities, the parameterized function is a Lyapunov function for the system. We propose calculating these vertex values using constructions from two classical converse Lyapunov theorems originally due to Yoshizawa and Massera. Numerical examples are presented to illustrate the proposed approach.     

用逼近方法建立代数无关性(Ⅱ)

设ｆ（ｘ）是以ａｎｘ为元素的连分式,其中系数ａｎ是正代数数．应用［１］中的判别法则,在某些仅与ａｎ有关的条件下证明了对任何绝对值互异的非零实代数数ａ１,…,ａｓ值ｆ（ａ１）代数无关．还对某些实超越数建立了的代数无关性．