Solving fuzzy equations using evolutionary algorithms and neural nets

 In this paper we use evolutionary algorithms and neural nets to solve fuzzy equations. In Part I we: (1) first introduce our three solution methods for solving the fuzzy linear equation AˉXˉ + Bˉ= Cˉ; for Xˉ and (2) then survey the results for the fuzzy quadratic equations, fuzzy differential equations, fuzzy difference equations, fuzzy partial differential equations, systems of fuzzy linear equations, and fuzzy integral equations; and (3) apply an evolutionary algorithm to construct one of the solution types for the fuzzy eigenvalue problem. In Part II we: (1) first discuss how to design and train a neural net to solve AˉXˉ + Bˉ= Cˉ for Xˉ and (2) then survey the results for systems of fuzzy linear equations and the fuzzy quadratic.     

The addition to the ergodic theorem on probability MV-algebras with product

 This article deals with the prototype of the strong law of large numbers, with individual ergodic theorem on probability MV-algebras with product. Dedicated to Prof. Ján Jakubík on the occasion of his 80th birthday This research is supported by Grant 1/9056/02 1991 Mathematics Subject Classification: 28E10     

Inference under imprecise probability assessments

Under partial knowledge, the use of the precise probability might be misleading. However, it is possible to process imprecise assessments, such as comparative previsions or grades of previsions. Rules for checking their coherence with the theoretical model and for making inference are given. Sometimes the derived conclusions might provide us with a complete answer for a given problem. In any case, technical tools can measure the imprecision of the answer and reveal if the analysis is thorough enough.     

Troubleshooting: NP-hardness and solution methods

 Troubleshooting is one of the areas where Bayesian networks are successfully applied [9]. In this paper we show that the generally defined troubleshooting task is NP-hard. We propose a heuristic function that exploits the conditional independence of all actions and questions given the fault of the device. It can be used as a lower bound of the expected cost of repair in heuristic algorithms searching an optimal troubleshooting strategy. In the paper we describe two such algorithms: the depth first search algorithm with pruning and the AO^* algorithm. RID="*" ID="*" The authors were supported through grant #87.2 of National Centre for IT Research, Denmark and through grant MSMT VS96008 from the Ministry of Education, Youth and Sports of the Czech Republic. We would like to thank Finn Verner Jensen for inspiring us to work on the discussed problem and for many valuable comments on this paper. We are grateful to Claus Skaanning for the detailed explanation of the BATS troubleshooter approach and to anonymous reviewers for helpful suggestions.     

On the conditional expectation on probability MV-Algebras with product

 In this paper the conditional expectation is defined and a variant of the martingale convergence theorem on probability MV-algebras with product is proved.     

Locally strong coherence and inference with lower–upper probabilities

 We introduce an operational way to reduce the spatial complexity in inference processes based on conditional lower–upper probabilities assessments. To reach such goal we must suitably exploit zero probabilities taking account of logical conditions characterizing locally strong coherence. We actually re-formulate for conditional lower–upper probabilities the notion of locally strong coherence already introduced for conditional precise probabilities. Thanks to the characterization, we avoid to build all atoms, so that several real problems become feasible. In fact, the real complexity problem is connected to the number of atoms. Since for an inferential process with lower–upper probabilities several sequences of constraints must be fulfilled, our simplification can have either a “global” or a “partial” effect, being applicable to all or just to some sequences. The whole procedure has been implemented by XLisp-Stat language. A comparison with other approaches will be done by an example. The contribution of L. Galli has been essentially addressed to some aspects of the algorithm's implementation.     

Learning Bayesian networks using various datasources and applications to financial analysis

 This paper illustrates opportunities of using Bayesian networks in fundamental financial analysis. In it, we will present an application based on construction of a Bayesian network from a database of financial reports collected for the years 1993–97. We will focus on one sector of the Czech economy – engineering – presenting an example that use the constructed Bayesian network in the sector financial analysis. In addition, we will deal with the rating analysis and show how to perform this kind of analysis by means of neural and Bayesian networks. This work was supported by the grant VS96008 of the Ministry of Education of the Czech Republic.     

Protocol synthesis and re-synthesis with optimal allocation of resources based on extended Petri nets

Protocol synthesis is used to derive a protocol specification, that is, the specification of a set of application components running in a distributed system of networked computers, from a specification of services (called the service specification) to be provided by the distributed application to its users. Protocol synthesis reduces design costs and errors by specifying the message exchanges between the application components, as defined by the protocol specification. In general, maintaining such a distributed application involves applying frequent minor modifications to the service specification due to changes in the user requirements. Deriving the protocol specification after each modification using the existing synthesis methods is considered expensive and time consuming. Moreover, we cannot identify what changes we should make to the protocol specification in correspondence to the changes in the service specification. In this paper, we present a new synthesis method to re-synthesize only those parts of the protocol specification that must be modified in order to satisfy the changes in the service specification. The method consists of a set of simple rules that are applied to the protocol specification written in an extended Petri net model. An application example is given along with some experimental results. Received: July 2001 / Accepted: July 2002 RID="*" ID="*" Supported by International Communications Foundation (ICF), Japan RID="**" ID="**" Supported by Communications and Information Technology Ontario (CITO) and Natural Sciences and Engineering Research Council (NSERC), Canada RID="*" ID="*" Supported by International Communications Foundation (ICF), Japan     

Feedforward networks with fuzzy signals

 The paper discusses feedforward neural networks with fuzzy signals. We analyze the feedforward phase and show some properties of the output function. Then we present a backpropagation like adaptation algorithm for crisp weights, thresholds and neuron slopes of the multilayer network with sigmoidal transfer functions. We provide theoretical justification for the adaptation formulas. The results are of general nature and together with the presented approach can be used for other types of feedforward networks. Proposed and discussed are also applications of the presented feedforward networks.     

A Neuro-Genetic Algorithm for Heteroskedastic Time-Series Processes Empirical Tests on Global Asset Returns

 The paper proposes a new neuro-genetic hybrid algorithm (NGHA) for coping with ill-conditioned time-series processes. Extensive testing and comparisons to various heteroskedastic models indicate that the neuro-genetic algorithm may be a useful device for modelling complicated time series. NGHA is used to model a factor price series corresponding to the European factor of a representative set of global asset returns. NGHA provides a platform for adapting evolutionary computation to the search for suitable networks for observed time series.     

Practical implementation of possibilistic probability mass functions

 Probability assessments of events are often linguistic in nature. We model them by means of possibilistic probabilities (a version of Zadeh's fuzzy probabilities with a behavioural interpretation) with a suitable shape for practical implementation (on a computer). Employing the tools of interval analysis and the theory of imprecise probabilities we argue that the verification of coherence for these possibilistic probabilities, the corrections of non-coherent to coherent possibilistic probabilities and their extension to other events and gambles can be performed by finite and exact algorithms. The model can furthermore be transformed into an imprecise first-order model, useful for decision making and statistical inference.     

Iterative Learning Control for Discrete-time Stochastic Systems with Quantized Information

An iterative learning control (ILC) algorithm using quantized error information is given in this paper for both linear and nonlinear discrete-time systems with stochastic noises. A logarithmic quantizer is used to guarantee an adaptive improvement in tracking performance. A decreasing learning gain is introduced into the algorithm to suppress the effects of stochastic noises and quantization errors. The input sequence is proved to converge strictly to the optimal input under the given index. Illustrative simulations are given to verify the theoretical analysis.      

Almost sure convergence of iterative learning control for stochastic systems

This paper proposes an iterative learning control (ILC) algorithm with the purpose of controling the output of a linear stochastic system presented in state space form to track a desired realizable trajectory. It is proved that the algorithm converges to the optimal one a.s. under the condition that the product input-output coupling matrices are full-column rank in addition to some assumptions on noises. No other knowledge about system matrices and covariance matrices is required.     

The Sample Complexity of Learning Fixed-Structure Bayesian Networks

We consider the problem of PAC learning probabilistic networks in the case where the structure of the net is specified beforehand. We allow the conditional probabilities to be represented in any manner (as tables or specialized functions) and obtain sample complexity bounds for learning nets with and without hidden nodes.     

Some Comments on Sequencing with Controllable Processing Times

Received March 30, 2001; revised October 22, 2001     

Naive Bayesian Classifier在遥感影像分类中的应用研究

将Naive Bayesian Classifier（简单贝叶斯网络分类器）用于遥感影像的分类,并对其主要问题如特征选择和后验概率推理等展开研究。使用K2结构学习算法选出具有类别可分性的波段,进一步利用互信息测试对遥感波段之间的相关性做分析,去除冗余信息。特征（波段）的条件独立性假设简化了联合概率的计算,以较小的计算代价获得后验概率。在此基础上,将Naive Bayesian Classifier用于多光谱和高光谱影像的分类,获得很好的性能和相当高的稳健性。     

Coherence checking and propagation of lower probability bounds

 In this paper we use imprecise probabilities, based on a concept of generalized coherence (g-coherence), for the management of uncertain knowledge and vague information. We face the problem of reducing the computational difficulties in g-coherence checking and propagation of lower conditional probability bounds. We examine a procedure, based on linear systems with a reduced number of unknowns, for the checking of g-coherence. We propose an iterative algorithm to determine the reduced linear systems. Based on the same ideas, we give an algorithm for the propagation of lower probability bounds. We also give some theoretical results that allow, by suitably modifying our algorithms, the g-coherence checking and propagation by working with a reduced set of variables and/or with a reduced set of constraints. Finally, we apply our algorithms to some examples. RID="*" ID="*" This paper is a revised and substantially extended version of a previous paper by the same authors, appeared in the Proc. of the 5th Workshop on Uncertainty Processing (WUPES'2000), Jindřichu̇v Hradec, Czech Republic, June 21–24, 1–13, 2000.     

The Design and Implementation of a Mobile Learning Resource

The convergence of mobile communications and handheld computers offers the opportunity to develop technology that will assist individuals and groups to learn anytime, anywhere. We describe the theory-informed design, implementation and evaluation of a handheld learning device. It is intended to support children to capture everyday events such as images, notes and sounds, to relate them to web-based learning resources, to organise these into a visual knowledge map, and to share them with other learners and teachers. A working prototype system, for children aged 9–11, is discussed and evaluated, as an exemplar of personal mobile systems for life-long learning.