Rough sets for pattern classification using pairwise-comparison-based tables

Rough set theory is a useful mathematical tool to deal with vagueness and uncertainty in available information. The results of a rough set approach are usually presented in the form of a set of decision rules derived from a decision table. Because using the original decision table is not the only way to implement a rough set approach, it could be interesting to investigate possible improvement in classification performance by replacing the original table with an alternative table obtained by pairwise comparisons among patterns. In this paper, a decision table based on pairwise comparisons is generated using the preference relation as in the Preference Ranking Organization Methods for Enrichment Evaluations (PROMETHEE) methods, to gauges the intensity of preference for one pattern over another pattern on each criterion before classification. The rough-set-based rule classifier (RSRC) provided by the well-known library for the Rough Set Exploration System (RSES) running under Windows as been successfully used to generate decision rules by using the pairwise-comparisons-based tables. Specifically, parameters related to the preference function on each criterion have been determined using a genetic-algorithm-based approach. Computer simulations involving several real-world data sets have revealed that of the proposed classification method performs well compared to other well-known classification methods and to RSRC using the original tables.     

New fitness sharing approach for multi-objective genetic algorithms

A novel fitness sharing method for MOGA (Multi-Objective Genetic Algorithm) is proposed by combining a new sharing function and sided degradations in the sharing process, with preference to either of two close solutions. The modified MOGA adopting the new sharing approach is named as MOGAS. Three different variants of MOGAS are tested; MOGASc, MOGASp and MOGASd, favoring children over parents, parents over children and solutions closer to the ideal point, respectively. The variants of MOGAS are compared with MOGA and other state-of-the-art multi-objective evolutionary algorithms such as IBEA, HypE, NSGA-II and SPEA2. The new method shows significant performance improvements from MOGA and is very competitive against other Evolutionary Multi-objective Algorithms (EMOAs) for the ZDT and DTLZ test functions with two and three objectives. Among the three variants MOGASd is found to give the best results for the test problems.     

A preference disaggregation decision support system for financial classification problems

Classification is one of the most extensively studied problems in the fields of multivariate statistical analysis, operations research and artificial intelligence. Decisions involving a classification of the alternative solutions are of major interest in finance, since several financial decision problems are best studied by classifying a set of alternative solutions (firms, loan applications, investment projects, etc.) in predefined classes. This paper proposes an alternative approach to the classical statistical methodologies that have been extensively used for the study of financial classification problems. The proposed methodology combines the preference disaggregation approach (a multicriteria decision aid method) with decision support systems. More specifically, the FINancial CLASsification (FINCLAS) multicriteria decision support system is presented. The system incorporates a plethora of financial modeling tools, along with powerful preference disaggregation methods that lead to the development of additive utility models for the classification of the considered alternatives into predefined classes. An application in credit granting is used to illustrate the capabilities of the system.     

Switched modified function projective synchronization of hyperchaotic Qi system with uncertain parameters

This work is involved with switched modified function projective synchronization of two identical Qi hyperchaotic systems using adaptive control method. Switched synchronization of chaotic systems in which a state variable of the drive system synchronize with a different state variable of the response system is a promising type of synchronization as it provides greater security in secure communication. Modified function projective synchronization with the unpredictability of scaling functions can enhance security. Recently formulated hyperchaotic Qi system in the hyperchaotic mode has an extremely broad frequency bandwidth of high magnitudes, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications. By Lyapunove stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems modified function projective synchronized. Synchronization under the effect of noise is also considered. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.     

结构可靠性分析的支持向量机方法

针对结构可靠性分析中功能函数不能显式表达的问题,将支持向量机方法引入到结构可靠性分析中．支持向量机是一种实现了结构风险最小化原则的分类技术,它具有出色的小样本学习性能和良好的泛化性能,因此提出了两种基于支持向量机的结构可靠性分析方法．与传统的响应面法和神经网络法相比,支持向量机可靠性分析方法的显著特点是在小样本下高精度地逼近函数,并且可以避免维数灾难．算例结果也充分表明支持向量机方法可以在抽样范围内很好地逼近真实的功能函数,减少隐式功能函数分析（通常是有限元分析）的次数,具有一定的工程实用价值．     

Multiple levels of preference in interactive strategic decisions

A multiple-level preference ranking structure is developed within the paradigm of the Graph Model for Conflict Resolution to study multi-objective decision making in conflict situations more realistically. In this structure, a decision maker may have multiple levels of preference for one state or scenario over another; for example, if state A is preferred to state B, it may be mildly preferred at level 1, more strongly preferred at level 2, …, or maximally preferred at level r, where r>0 is a fixed parameter. The number of levels, r, is unrestricted in this system, thereby extending earlier two-level (r=1) and three-level (r=2) structures. Multilevel versions of four stability definitions, Nash stability, general metarationality, symmetric metarationality, and sequential stability, are defined for the graph model with this extended preference structure, and the relationships among them are investigated. A specific case study, including multiple decision makers and multiple levels of preference, is carried out to illustrate how the new solution concepts can be applied in practice.     

Interval fuzzy preferences in the graph model for conflict resolution

A new analysis technique, appropriate to situations of high preference uncertainty, is added to the graph model for conflict resolution methodology. Interval fuzzy stabilities are now formulated, based on decision makers’ (DMs’) interval fuzzy preferences over feasible scenarios or states in a conflict. Interval fuzzy stability notions enhance the applicability of the graph model, and generalize its crisp and fuzzy preference-based stability ideas. A graph model is both a formal representation and an analysis procedure for multiple participant-multiple objective decisions that employs stability concepts representing various forms of human behavior under conflict. Defined based on a type-2 fuzzy logic, an interval fuzzy preference for one state over another is represented by a subinterval of [0, 1] indicating an interval-valued preference degree for the first state over the second. The interval fuzzy stabilities put forward in this research are interval fuzzy Nash stability, interval fuzzy general metarational stability, interval fuzzy symmetric metarational stability, and interval fuzzy sequential stability. A state is interval fuzzy stable for a DM if moving to any other state is not adequately desirable to the DM; where adequacy is measured by the interval fuzzy satisficing threshold of the DM and farsightedness, involving possible moves and countermoves by DMs, is determined by the interval fuzzy stability notion selected. Note that infinitely many degrees in an interval-valued preference are preserved in characterizing the desirability of a move. A state from which no DM can move to any sufficiently desirable scenario is an interval fuzzy equilibrium, and is interpreted as a possible resolution of the strategic conflict under study. The new stability concept is illustrated through its application to an environmental conflict that took place in Elmira, Ontario, Canada. Insightful results are identified and discussed.     

食品卫生安全保障体系数学模型的研究

主要针对食品安全保障体系中的食物摄入量模型、污染物分布模型和风险评估模型做了以下研究:提出一种基于多层次划分法的抽样方案设计抽样,针对食品的分类问题,提出一种基于贡献率的食品分类法;提出利用广义g·h分布估计污染物的偏态分布的方法;进一步基于Bootstrap法提出了一种利用少量数据再抽样估计偏态分布特性的方法;提出一种尾部放大法,巧妙地将概率搜索和理论分析相结合,实现高精度地估计污染物摄入量的右分位点.此外,对相关的几个理论问题进行研究,并基于Monte-Carlo模拟给出相应的解决方案.     

Order reduction and determination of dominant state variables of nonlinear systems

The method presented can simplify nonlinear system models by reducing the number of state equations. Starting from a special state space representation, the main idea is to take over all nonlinear terms into the reduced system and to renew all couplings of state variables, input variables and nonlinear functions. The steady state performance can be influenced by additional measures which are discussed in detail and which are illustrated by a technical example. A dominance analysis is introduced which helps choosing the system order and the dominant state variables. All computations are based on proven algorithms and most of them are free of iterations.     

Environmental site evaluation of waste management facilities embedded into EUGÈNE model: A multicriteria approach

EUGÈNE is a sophisticated mixed integer linear programming model developed to help regional decision makers on long-term planning for solid waste management activities. The model removes almost every limitations encountered in other waste management models and contains a large quantity of variables and constraints. The method used to embed waste management environmental parameters in the EUGÈNE model consists in building global impact index (GII) for all site/facility combinations. First, an environmental and spatial evaluation of waste management facilities over sites is based on qualitative and quantitative criteria measuring biophysical and social impacts. Spatial analysis is carried out by geographical information system routines. Then, a multicriteria analysis ranks all site/facility combinations, according to their global performance based on all criteria. The net flow, computed by the PROMETHEE multicriteria outranking method, is considered as a GII to be embedded into EUGÈNE. The model objective function is thus modified to minimize total system cost and GII. Some practical results obtained for the City of Montreal are discussed.     

食品卫生安全保障体系数学模型及改进问题研究

论文研究了食品卫生安全保障体系的数学模型,阐述了各种模型的建立方法.在建模过程中,探讨解决了一些改进模型的理论问题.主要工作包括:1、通过改进CAC食品分类标准,给出了一种有效的适用于抽样调查的食物分类方法,在此基础上建立了膳食模型;2、给出了污染物分布模型及建模方法,提出了一种由少量样本数据迭代地外推随机变量整体概率密度函数的算法,讨论了由不同区域的监测数据估计全国总体分布的问题,并给出了一种解决方案;3、建立了风险评估模型,探讨了输入数据不配套时,抽样调查数据的衔接问题.提出了一种新的污染物摄入量的99.999%的右分位点的估计方法.     

Selection of a representative value function in robust multiple criteria ranking and choice

We introduce the concept of a representative value function in robust ordinal regression applied to multiple criteria ranking and choice problems. The proposed method can be seen as a new interactive UTA-like procedure, which extends the UTA^GMS and GRIP methods. The preference information supplied by the decision maker (DM) is composed of a partial preorder and intensities of preference on a subset of reference alternatives. Robust ordinal regression builds a set of general additive value functions which are compatible with the preference information, and returns two binary preference relations: necessary and possible. They identify recommendations which are compatible with all or at least one compatible value function, respectively. In this paper, we propose a general framework for selection of a representative value function from among the set of compatibles ones. There are a few targets which build on results of robust ordinal regression, and could be attained by a representative value function. In general, according to the interactively elicited preferences of the DM, the representative value function may emphasize the advantage of some alternatives over the others when all compatible value functions acknowledge this advantage, or reduce the ambiguity in the advantage of some alternatives over the others when some compatible value functions acknowledge an advantage and other ones acknowledge a disadvantage. The basic procedure is refined by few extensions. They enable emphasizing the advantage of alternatives that could be considered as potential best options, accounting for intensities of preference, or obtaining a desired type of the marginal value functions.     

Experiments with an interactive paired comparison simplex method for molp problems

In this paper, an interactive paired comparison simplex based method formultiple objective linear programming (MOLP) problems is developed and compared to other interactive MOLP methods. The decision maker (DM)’s utility function is assumed to be unknown, but is an additive function of his known linearized objective functions. A test for ‘utility efficiency’ for MOLP problems is developed to reduce the number of efficient extreme points generated and the number of questions posed to the DM. The notion of ‘strength of preference ’ is developed for the assessment of the DM’s unknown utility function where he can express his preference for a pair of extreme points as ‘strong ’, ‘weak ’, or ‘almost indifferent ’. The problem of ‘inconsistency of the DM’ is formalized and its resolution is discussed. An example of the method and detailed computational results comparing it with other interactive MOLP methods are presented. Several performance measures for comparative evaluations of interactive multiple objective programming methods are also discussed. All rights reserved. This study, or parts thereof, may not be reproduced in any form without written permission of the authors.     

A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification

In this paper, we present two control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with immeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples including a real circuit system are given to demonstrate the effectiveness of the presented design methodologies.     

一致稳定合作系统的全局稳定性

本文讨论了一类合作系统的解的收敛性.其基本假设是Jacobi矩阵在中一致稳定．在这个假设下,我们对这类系统给出了完整的全局性态．本文的主要结果如下：如果系统有一个正平衡点,那么它在Int中全局渐近稳定,并给出了系统的非负平衡点全局渐近稳定的充分必要条件．     

Numerical methods for structured population models: The Escalator Boxcar Train

A numerical integration method is introduced for the class of hyperbolic partial differential equations that occur in physiologically structured population models. These equations describe the time evolution of the population density-function over the individual state-space Ω. Exploiting the biological interpretation of the equation, this density-function is represented by a set of moments over a collection of subdomains in Ω, moving along the characteristics of the partial differential equation (PDE). These moments are readily interpreted as numbers of individuals in a cohort, mean individual state in a cohort, etc. The numerical method consists of approximating the differential equations. The method appears to be very efficient for this special type of PDE. It combines such desirable properties as as lack of dispersion and dissipation and a preservation of monotonicity of the density function along the characteristics with a strong relation to the biological background of the equations for these moments to arrive at a closed system of ordinary differential equations. The method also allows one to incorporate the usual type of nonlinearities that occur in physiologically structured population models. A numerical example is presented as an illustration of the application of the method.     

考虑专家偏好的创新型企业创新能力评价方法

为解决创新型企业创新能力评价过程中专家偏好差异和指标量纲不一致等问题,文章构建了一个科学的评价指标体系,运用考虑专家偏好的效用函数对创新能力评价指标进行效用估算,并计算灰色关联系数;最后运用TOPSIS方法对创新型企业的创新能力进行综合评价和排序。数值实例证明了该方法的科学性和实用性。     

Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure

A new method for predicting failures of a partially observable system is presented. System deterioration is modeled as a hidden, 3-state continuous time homogeneous Markov process. States 0 and 1, which are not observable, represent good and warning conditions, respectively. Only the failure state 2 is assumed to be observable. The system is subject to condition monitoring at equidistant, discrete time epochs. The vector observation process is stochastically related to the system state. The objective is to develop a method for optimally predicting impending system failures. Model parameters are estimated using EM algorithm and a cost-optimal Bayesian fault prediction scheme is proposed. The method is illustrated using real data obtained from spectrometric analysis of oil samples collected at regular time epochs from transmission units of heavy hauler trucks used in mining industry. A comparison with other methods is given, which illustrates effectiveness of our approach.     

Compound modification of globoidal worm drive with variable parameters

The meshing theory is built for the globoidal worm drive systematically. Several modification parameters, including the center distance, the transmitting ratio and the height of the cutter frame, are taken into account concurrently and they are all variable. Many types of modification in the foregoing study can be viewed as the special cases of this work. A new method is proposed to obtain the velocity ratio modification function. The height modification function is recommended to adopt a linear function, whose coefficients may be determined by the trial method. The meshing function of the worm pair is deduced by virtue of the vector rotation approach. In the case of the modification with single constant parameter, the classification standard of the drive type is proved strictly. The computing methods of the contact zone, the contact line, and the instantaneous meshing point are expounded explicitly. The reason why a globoidal worm drive can implement the double-line contact between the teeth is uncovered clearly. The reason why a modified globoidal worm gearing can shun the curvature interference is discovered. The comparative researches on the mesh characters of the diverse modified drives are implemented adequately. Some kinds of the modified drive, containing the compound modified drive with variable parameters, are recommended to be utilized in practice for the excellent mesh performances.     

Power-series approximations for the optimal feedback control of noisy nonlinear systems

Power-series methods are developed for designing approximately optimal state regulators for a nonlinear system subject to white Gaussian random disturbances. The performance index of the control is an ensemble average of a quadratic form. A perfect observation of the system state is assumed. When the system nonlinearity is small and it is characterized by a polynomial function of the state, a definite method is presented to construct a suboptimal feedback control of a power-series form in a small nonlinearity parameter. If the variance of noise is small, an alternative method is also applicable which yields a suboptimal control in a power series with respect to a variance parameter. A simple one-dimensional problem is examined to make comparison between controls of the two different forms.