Rough set approach to multiple criteria classification with imprecise evaluations and assignments

Dominance-based Rough Set Approach (DRSA) has been introduced to deal with multiple criteria classification (also called multiple criteria sorting, or ordinal classification with monotonicity constraints), where assignments of objects may be inconsistent with respect to dominance principle. In this paper, we consider an extension of DRSA to the context of imprecise evaluations of objects on condition criteria and imprecise assignments of objects to decision classes. The imprecisions are given in the form of intervals of possible values. In order to solve the problem, we reformulate the dominance principle and introduce second-order rough approximations. The presented methodology preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and precisiation. Moreover, the meaning of the precisiation property is extended to the considered case. The paper presents also a way to reduce decision tables and to induce decision rules from rough approximations.     

Bayesian predictive densities based on superharmonic priors for the 2-dimensional Wishart model

Bayesian predictive densities for the 2-dimensional Wishart model are investigated. The performance of predictive densities is evaluated by using the Kullback–Leibler divergence. It is proved that a Bayesian predictive density based on a prior exactly dominates that based on the Jeffreys prior if the prior density satisfies some geometric conditions. An orthogonally invariant prior is introduced and it is shown that the Bayesian predictive density based on the prior is minimax and dominates that based on the right invariant prior with respect to the triangular group.     

Contact Transformation Group Classification of Nonlinear Wave Equations

Interest in nonlinear wave equations has been stimulated bynumerous physical applications, such as telecommunication (e.g.nonlinear telegrapher equation), gasdynamics, anisotropic plasticity andnonlinear elasticity, etc. Mathematical models of these phenomena canoften be reduced to particular types of the equation u _tt = f(x, u _x ) u _xx + g(x, u _x ). In this paper, the problem ofclassification of the latter equation with respect to admitted contacttransformation groups is reduced to the investigation of pointtransformation groups of the equivalent system of first-orderquasi-linear equations v _t =a(x, v)w _x , w _t = b(x,v)v _x .     

Asynchronous cellular automata and pattern classification

This article designs an efficient two‐class pattern classifier utilizing asynchronous cellular automata (ACAs). The two‐state three‐neighborhood one‐dimensional ACAs that converge to fixed points from arbitrary seeds are used here for pattern classification. To design the classifier, (1) we first identify a set of ACAs that always converge to fixed points from any seeds, (2) each ACA should have at least two but not huge number of fixed point attractors, and (3) the convergence time of these ACAs are not to be exponential. To address the second issue, we propose a graph, coined as fixed point graph of an ACA that facilitates in counting the fixed points. We further perform an experimental study to estimate the convergence time of ACAs, and find there are some convergent ACAs which demand exponential convergence time. Finally, we identify there are 73 (out of 256) ACAs which can be effective candidates as pattern classifier. We use each of the candidate ACAs on some standard datasets, and observe the effectiveness of each ACAs as pattern classifier. It is observed that the proposed classifier is very competitive and performs reliably better than many standard existing classifier algorithms. © 2016 Wiley Periodicals, Inc. Complexity 21: 370–386, 2016     

一类Block型李代数的分类和中心扩张

本文我们决定了一类Block型李代数$\BB$在同构意义下的分类和中心扩张, 其中$q$是一个非零复数. 我们的结果推广了以前的一些结果.     

浙江省7个地点桃花水母的形态学分类研究

以2003~2008年采集的浙江省宁波、杭州、温州和金华4个地区7个地点的桃花水母为研究对象,通过传统分类方法(形态特征分类),对桃花水母的伞径、触手数目和级数、主辐触手和其他触手的长度比、刺丝囊疣形状和排列、平衡囊数目和形状以及生殖腺的形状和颜色等生物特征的观察,将其定为索氏桃花水母(Craspedacusta sowerbyi),其中金华永康和温州平阳2个地点的桃花水母定为永康桃花水母亚种(C.sowerbyi yongkangensis),宁波、杭州5个地点的桃花水母为信阳桃花水母亚种(C.sowerbyi xinyangensis).     

由定子电流信号分析陀螺电机滚珠轴承故障诊断与分类（英文）

在陀螺电机中,轴承故障是最普遍的失效形式。针对陀螺电机球轴承中各组成部分出现故障难以区分,而更换整套轴承又造成巨大浪费的问题,提出了一种基于电流信号分析的陀螺电机轴承故障分类方法。该方法通过采集定子电流信号,并应用数学分析工具,提取出定子电流的特征信号。通过使用顺序递推法排除了冗余和无效特征,然后用最佳的特征信号建立特征空间。通过使用隐马尔科夫模型,对轴承的典型故障(外环故障、内环故障、球故障和保持架故障)进行了准确的分类。该方法的有效性在一台具有不同轴承故障的直流无刷陀螺电机上得到验证,实验结果显示分类的正确率达到97.1%。     

Comment on “Group analysis of KdV equation with time dependent coefficients”

We show that the group classification results of the article entitled “Group analysis of KdV equation with time dependent coefficients” which appeared in [A.G. Johnpillai, M.C. Khalique, Group analysis of KdV equation with time dependent coefficients, Appl. Math. Comput. 216 (2010) 3761-3771] can be obtained from those of a more general class by a change of variables.     

Emergence of density dynamics by surface interpolation in elementary cellular automata

A classic problem in elementary cellular automata (ECAs) is the specification of numerical tools to represent and study their dynamical behaviour. Mean field theory and basins of attraction have been commonly used; however, although the first case gives the long term estimation of density, frequently it does not show an adequate approximation for the step-by-step temporal behaviour; mainly for non-trivial behaviour. In the second case, basins of attraction display a complete representation of the evolution of an ECA, but they are limited up to configurations of 32 cells; and for the same ECA, one can obtain tens of basins to analyse. This paper is devoted to represent the dynamics of density in ECAs for hundreds of cells using only two surfaces calculated by the nearest-neighbour interpolation. A diversity of surfaces emerges in this analysis. Consequently, we propose a surface and histogram based classification for periodic, chaotic and complex ECA.     

An improvement to multiple criteria ABC inventory classification

In this paper we presented an extended version of the Ng-modelg [W.L. Ng, A simple classifier for multiple criteria ABC analysis, European Journal of Operational Research 177 (2007) 344–353] for multi-criteria inventory classification. The proposed model is a nonlinear programming model which determines a common set of weights for all the items. Our model not only incorporates multiple criteria for ABC classification, but also maintains the effects of weights in the final solution, an improvement over the model proposed by Ng. An illustrative example is presented to compare our model and the Ng-model.