Fuzzy regression analysis using neural networks

In this paper, we propose simple but powerful methods for fuzzy regression analysis using neural networks. Since neural networks have high capability as an approximator of nonlinear mappings, the proposed methods can be applied to more complex systems than the existing LP based methods. First we propose learning algorithms of neural networks for determining a nonlinear interval model from the given input-output patterns. A nonlinear interval model whose outputs approximately include all the given patterns can be determined by two neural networks. Next we show two methods for deriving nonlinear fuzzy models from the interval model determined by the proposed algorithms. Nonlinear fuzzy models whose h-level sets approximately include all the given patterns can be derived. Last we show an application of the proposed methods to a real problem.     

Beat patrolling in urban areas A case study

Urban police patrol work has been analysed in the present paper. Working on the crime-rate, as reported by the police department, a plan has been worked out to ensure an effective police patrol in a given locality. This locality is predominantly a “business/marketing area”. Many problems connected with beat patrol like type of beat, route numbers, beat-ranking and others have been discussed. The analysis will help the police station to understand the beat patrol problem. Alternative beat routes have been suggested, together with deployment. Beat ranking may help in assessing the vulnerability of an area and as such proper steps may be taken in advance to prevent the occurrence of the crime. It is expected that patrolling will be more effective and useful after the implementation of this study.     

A genetic algorithm with neural network fitness function evaluation for IMRT beam angle optimization

Intensity Modulated Radiotherapy Treatment (IMRT) is a technique used in the treatment of cancer, where the radiation beams are modulated by a multileaf collimator allowing the irradiation of the patient using non-uniform radiation fields from selected angles. Beam angle optimization consists in trying to find the best set of angles that should be used in IMRT planning. The choice of this set of angles is patient and pathology dependent and, in clinical practice, most of the times it is made using a trial and error procedure or simply using equidistantly distributed angles. In this paper we propose a genetic algorithm that aims at calculating good sets of angles in an automated way, given a predetermined number of angles. We consider the discretization of all possible angles in the interval [0 \(^{\circ }\) , 360 \(^{\circ }\) ], and each individual is represented by a chromosome with 360 binary genes. As the calculation of a given individual’s fitness is very expensive in terms of computational time, the genetic algorithm uses a neural network as a surrogate model to calculate the fitness of most of the individuals in the population. To explicitly consider the estimation error that can result from the use of this surrogate model, the fitness of each individual is represented by an interval of values and not by a single crisp value. The genetic algorithm is capable of finding improved solutions, when compared to the usual equidistant solution applied in clinical practice. The genetic algorithm will be described and computational results will be shown.     

求解线性约束的区间二次规划问题的神经网络

在本文中,基于神经网络,提出了一类求解具有线性约束区间二次规划问题的方法,使用增广拉格朗日函数,建立了求解规划问题的神经网络模型。基于压缩不动点理论,证明了所提出神经网络的平衡点就是等式约束区间二次规划问题的最优解。使用适当的Lyapunov函数,证明了所提出的神经网络的平衡点是全局指数稳定的。最后,两个数值仿真结果验证了本文所用方法的可行性与有效性。     

Exponential stability analysis for uncertain neural networks with interval time-varying delays

In this paper, the problem of exponential stability analysis for neural networks is investigated. It is assumed that the considered neural networks have norm-bounded parametric uncertainties and interval time-varying delays. By constructing a new Lyapunov functional, new delay-dependent exponential stability criteria with an exponential convergence rate are established in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the effectiveness of proposed criteria.     

A hybrid intelligent system for predicting bank holding structures

A composite model of neural network and rough sets components was constructed to predict a sample of bank holding patterns. The final model was able to correctly classify 96% of a testing set of four types of bank holding structures. Holding structure is defined as the number of banks under common ownership. For this study, forms of bank holding structure include: banks that are not owned by another company, single banks that are held by another firm, pairs of banks that are held by another enterprise, and three or more banks that are held by another company. Initially, input to the neural network model was 28 financial ratios for more than 200 banks in Arkansas for 1992. The 28 ratios are organized by categories such as liquidity, credit risk, leverage, efficiency, and profitability. The ratios were constructed with 70 bank variables such as net worth, deposits, total assets, net loans, total operating income, etc. The first neural network model correctly classified 84% of the testing set at a tolerance level of 0.20. Another artificial intelligence (AI) procedure known as two-dimensional rough sets was then applied to the dataset. Rough sets reduced the number of input variables from 28 to 18, a drop of 36% in the number of input variables. This version of rough sets also eliminated a number of records, thereby reducing the information system (i.e., matrix) on both vertical and horizontal dimensions. A second neural network was trained with the reduced number of input variables and records. This network correctly classified 96% of the testing set at a tolerance level of 0.20, an increase of 11% in the accuracy of the prediction. By applying two-dimensional reducts to the dataset of financial ratios, the predictive accuracy of the neural network model was improved substantially. Banking institutions that are prime candidates for mergers or acquisitions can then be more accurately identified through the use of this hybrid decision support system (DSS) which combines different types of AI techniques for the purposes of data management and modeling.     

Global exponential stability for interval general bidirectional associative memory (BAM) neural networks with proportional delays

This paper is concerned with interval general bidirectional associative memory (BAM) neural networks with proportional delays. Using appropriate nonlinear variable transformations, the interval general BAM neural networks with proportional delays can be equivalently transformed into the interval general BAM neural networks with constant delays. The sufficient condition for the existence and uniqueness of equilibrium point of the model is established by applying Brouwer's fixed point theorem. By constructing suitable delay differential inequalities, some sufficient conditions for the global exponential stability of the model are obtained. Two examples are given to illustrate the effectiveness of the obtained results. This paper ends with a brief conclusion. Copyright © 2016 John Wiley & Sons, Ltd.     

Exponential stability criteria for discrete-time recurrent neural networks with time-varying delay

In this paper, the robust global exponential stability is investigated for the discrete-time recurrent neural networks (RNNs) with time-varying interval delay. By choosing an augmented Lyapunov–Krasovskii functional, delay-dependent results guaranteeing the global exponential stability and the robust exponential stability of the concerned neural network are obtained. The results are shown to be a generalization of some previous results, and less conservative than the existing works. Two numerical examples are given to demonstrate the applicability of the proposed method.     

Almost periodicity for a class of delayed Cohen–Grossberg neural networks with discontinuous activations

The objective of this paper is to investigate the dynamics of a class of delayed Cohen–Grossberg neural networks with discontinuous neuron activations. By means of retarded differential inclusions, we obtain a result on the local existence of solutions, which improves the previous related results for delayed neural networks. It is shown that an M-matrix condition satisfied by the neuron interconnections, can guarantee not only the existence and uniqueness of an almost periodic solution, but also its global exponential stability. It is also shown that the M-matrix condition ensures that all solutions of the system display a common asymptotic behavior. In this paper, we prove that the existence interval of the almost periodic solution is (?∞, +∞), whereas the existence interval is only proved to be [0, +∞) in most of the literature. As special cases, we derive the results of existence, uniqueness and global exponential stability of a periodic solution for delayed neural networks with periodic coefficients, as well as the similar results of an equilibrium for the systems with constant coefficients. To the author’s knowledge, the results in this paper are the only available results on almost periodicity for Cohen–Grossberg neural networks with discontinuous activations and delays.     

Multiple criteria decision making method based on normal interval‐valued intuitionistic fuzzy generalized aggregation operator

On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval‐valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval‐valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval‐valued intuitionistic fuzzy weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval‐valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval‐valued intuitionistic fuzzy generalized weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval‐valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. © 2015 Wiley Periodicals, Inc. Complexity 21: 277–290, 2016     

混合区间多尺度分解的区间时间序列组合预测

鉴于传统预测方法一直基于“点”来衡量时间序列数据,然而现实生活中在给定的时间段内许多变量是有区间限制的,点值预测会损失波动性信息。因此,本文提出了一种基于混合区间多尺度分解的组合预测方法。首先,建立区间离散小波分解方法(IDWT)、区间经验模态分解方法(IEMD)和区间奇异普分析方法(ISSA)。其次,用本文构建的IDWT、IEMD和ISSA对区间时间序列进行多尺度分解,从而得到区间趋势序列和残差序列。然后,用霍尔特指数平滑方法(Holt's)、支持向量回归(SVR)和BP神经网络对区间趋势序列和残差序列进行组合预测得到三种分解方法下的区间时间序列预测值。最后,用BP神经网络对各预测结果进行集成得到区间时间序列最终预测值。同时,为证明模型的有效性进行了AQI空气质量的实证预测分析,结果表明,本文所提出基于混合区间多尺度分解的组合预测方法具有较高的预测精度和良好的适用性。     

On stability analysis for neural networks with interval time-varying delays via some new augmented Lyapunov–Krasovskii functional

This paper is concerned with the problem of stability analysis of neural networks with interval time-varying delays. It is assumed that the lower bound of time-varying delays is not restricted to be zero. By constructing a newly augmented Lyapunov–Krasovskii functional which has not been proposed yet and utilizing some integral information on activation function as elements of augmented vectors, an improved stability criterion with the framework of linear matrix inequalities (LMIs) is introduced in Theorem 1. Based on the result of Theorem 1 and utilizing the property of the positiveness of Lyapunov–Krasovskii functional, a further relaxed stability condition will be proposed in Theorem 2. The effectiveness and less conservatism of the proposed theorems will be illustrated via three numerical examples.     

Delay-dependent robust stability analysis for Markovian jumping stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the global asymptotical stability analysis problem is considered for a class of Markovian jumping stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. An alternative delay-dependent stability analysis result is established based on the linear matrix inequality (LMI) technique, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Neither system transformation nor free weight matrix via Newton–Leibniz formula is required. Two numerical examples are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing results in the literature.     

On brain fluctuations and the challenges ahead

The brain can be considered as a thermodynamic machine working out of equilibrium, crossed by a stationary (under normal conditions) flux of energy, that is dissipated through thermal fluctuations. The analogy with a fluid state suggests that long space–time correlations have to be present in such a machine to keep it in working conditions, thus making the brain effectively explore dynamical and statistical regimes characterized by scale-free properties. We argue that such a distinctive feature may emerge from an out-of-equilibrium thermodynamic approach and also from microscopic models (neural networks) with a suitable combination of phenomenological ingredients.     

基于非等时距加权灰色模型与神经网络的组合预测算法

非等时距预测算法在不等时间间隔序列的趋势分析与预测方面具有重要作用．在传统灰色预测理论的基础上,提出一种基于非等时距加权灰色模型和神经网络的组合预测算法．通过构建非等时距加权灰色预测模型,将原始数据序列的平均值作为累加序列初值,将连续累积函数的积分面积作为背景值,对累加序列进行加权处理,以真实反映时间序列发展对预测结果的影响．在此基础上,引入BP神经网络对灰色预测的残差序列进行修正,进一步提高了预测精度．经算例验证,该算法预测精度达到1级,且高于类似算法．     

Dynamic analysis of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks with discrete interval and distributed time-varying delays

In this paper, the dynamic analysis problem is considered for a new class of Markovian jumping impulsive stochastic Cohen–Grossberg neural networks (CGNNs) with discrete interval and distributed delays. The parameter uncertainties are assumed to be norm bounded and the discrete delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some asymptotic stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be easily calculated by LMI Toolbox in Matlab. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some existing results in the literature.     

New robust stability criteria for uncertain neural networks with interval time-varying delays

In this paper, problem of robust stability of uncertain neural networks with interval time-varying delays has been investigated. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the lower and upper bounds of the interval time-varying delays are available. Based on the Lyapunov–Krasovskii functional approach, a new delay-dependent stability criteria is presented in terms of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term

In this paper, the problem of passivity analysis is investigated for neutral type neural networks with Markovian jumping parameters and time delay in the leakage term. The delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. By constructing proper Lyapunov–Krasovskii functional, new delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). Moreover, it is well known that the passivity behavior of neural networks is very sensitive to the time delay in the leakage term. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed method.     

Stochastic approach to kinematic reliability of open-loop mechanism with dimensional tolerance

Open-loop mechanisms are usually employed in industrial applications to position or orient an object, where high accuracy, repeatability and stability of operations are required. Deviations in link dimensions and joint clearances in manufacturing and assembling operations decrease the degree of accuracy and repeatability of the systems. Due to the random nature of dimensional tolerance and clearance, a stochastic approach to figure out reliability of the open-loop mechanism should be required. In this work, firstly, with the assumption that all kinematical parameters are normally distributed random variables, stochastic model of links with dimensional tolerances and of revolute joints with clearances are presented. The kinematical reliability for the positioning and orientation repeatability is then calculated analytically based on an advanced first-order second moment (AFOSM) method and verified with a Monte Carlo simulation method. Finally, the proposed methods are numerically illustrated with an RRR spatial manipulator.     

Robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays

This paper investigates robust stability analysis for Markovian jumping interval neural networks with discrete and distributed time-varying delays. The parameter uncertainties are assumed to be bounded in given compact sets. The delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional (LKF), some inequality techniques and stochastic stability theory, new delay-dependent stability criteria have been obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the less conservative and effectiveness of our theoretical results.