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146
ANFIS: AdaptiveNetworkBased Fuzzy Inference System”,
 IEEE Trans. on System, Man and Cybernetics,
, 1993
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Nonlinear BlackBox Modeling in System Identification: a Unified Overview
 Automatica
, 1995
"... A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, ..."
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Cited by 225 (16 self)
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A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping from observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function e...
Functional Equivalence between Radial Basis Function Networks and Fuzzy Inference Systems
, 1993
"... This short article shows that under some minor restrictions, the functional behavior of radial basis function networks and fuzzy inference systems are actually equivalent. This functional equivalence implies that advances in each literature, such as new learning rules or analysis on representational ..."
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Cited by 169 (4 self)
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This short article shows that under some minor restrictions, the functional behavior of radial basis function networks and fuzzy inference systems are actually equivalent. This functional equivalence implies that advances in each literature, such as new learning rules or analysis on representational power, etc., can be applied to both models directly. It is of interest to observe that twomodels stemming from different origins turn out to be functional equivalent.
Generating an interpretable family of fuzzy partitions
 IEEE Transactions on Fuzzy Systems
, 2004
"... Abstract—In this paper, we propose a new method to construct fuzzy partitions from data. The procedure generates a hierarchy including best partitions of all sizes from n to two fuzzy sets. The maximum size is determined according to the data distribution and corresponds to the finest resolution lev ..."
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Cited by 30 (9 self)
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Abstract—In this paper, we propose a new method to construct fuzzy partitions from data. The procedure generates a hierarchy including best partitions of all sizes from n to two fuzzy sets. The maximum size is determined according to the data distribution and corresponds to the finest resolution level. We use an ascending method for which a merging criterion is needed. This criterion is based on the definition of a special metric distance suitable for fuzzy partitioning, and the merging is done under semantic constraints. The distance we define does not handle the point coordinates, but directly their membership degrees to the fuzzy sets of the partition. This leads to the introduction of the notions of internal and external distances. The hierarchical fuzzy partitioning is carried independently over each dimension, and, to demonstrate the partition potential, they are used to build fuzzy inference system using a simple selection mechanism. Due to the merging technique, all the fuzzy sets in the various partitions are interpretable as linguistic labels. The tradeoff between accuracy and interpretability constitutes the most promising aspect in our approach. Well known data sets are investigated and the results are compared with those obtained by other authors using different techniques. The method is also applied to real world agricultural data, the results are analyzed and weighed against those achieved by other methods, such as fuzzy clustering or discriminant analysis. Index Terms—Distance, fuzzy partitioning, interpretability, learning, rule induction. I.
A Reinforcement Learning Approach to Dynamic Resource Allocation. Sun Microsystems Laboratories
, 2005
"... This paper presents a general framework for performing adaptive reconfiguration of a distributed system based on maximizing the longterm business value, defined as the discounted sum of all future rewards and penalties. The problem of dynamic resource allocation among multiple entities sharing a co ..."
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Cited by 22 (5 self)
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This paper presents a general framework for performing adaptive reconfiguration of a distributed system based on maximizing the longterm business value, defined as the discounted sum of all future rewards and penalties. The problem of dynamic resource allocation among multiple entities sharing a common set of resources is used as an example. A specific architecture (DRAFRL) is presented, which uses the emerging methodology of reinforcement learning in conjunction with fuzzy rulebases to achieve the desired objective. This architecture can work in the context of existing resource allocation policies and learn the values of the states that the system encounters under these policies. Once the learning process begins to converge, the user can allow the DRAFRL architecture to make some additional resource allocation decisions or override the ones suggested by the existing policies so as to improve the longterm business value of the system. The DRAFRL architecture can also be deployed in an environment without any existing resource allocation policies. An implementation of the DRAFRL architecture in Solaris 10 demonstrated a robust performance improvement in the problem of dynamically migrating CPUs and memory blocks between three resource partitions so as to match the stochastically changing ∗ This material is based upon work supported by DARPA under Contract No. NBCH3039002. 1 workload in each partition, both in the presence and in the absence of resource migration costs.
Fuzzy Rule Based Modeling As A Universal Approximation Tool
, 1996
"... INTRODUCTION 1.1. WHY UNIVERSAL APPROXIMATION In some cases, fuzzy rule based model needs tuning. If we have applied some version of fuzzy rule based modeling, and the resulting model is satisfactory, great. But sometimes, the resulting model is not of very high quality: \Gamma we may have misint ..."
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Cited by 21 (14 self)
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INTRODUCTION 1.1. WHY UNIVERSAL APPROXIMATION In some cases, fuzzy rule based model needs tuning. If we have applied some version of fuzzy rule based modeling, and the resulting model is satisfactory, great. But sometimes, the resulting model is not of very high quality: \Gamma we may have misinterpreted some of the expert's rules; \Gamma we may have missed some of the important rules. So, to improve the quality of the resulting model, we must either: \Gamma reinterpret the existing rules, or \Gamma ask the experts for extra rules. 2 V. KREINOVICH ET AL. Before we start tuning, we want to make sure that tuning will help. In order to make sure that this "tuning" will always help, we must guarantee that by appropriate tuning, we will be able to change the initial (not very successful) model into a successful one. To guarantee that the fuzzy rule based modeling me
Fuzzy Finitestate Automata Can Be Deterministically Encoded into Recurrent Neural Networks
, 1996
"... There has been an increased interest in combining fuzzy systems with neural networks because fuzzy neural systems merge the advantages of both paradigms. On the one hand, parameters in fuzzy systems have clear physical meanings and rulebased and linguistic information can be incorporated into adapt ..."
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Cited by 20 (5 self)
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There has been an increased interest in combining fuzzy systems with neural networks because fuzzy neural systems merge the advantages of both paradigms. On the one hand, parameters in fuzzy systems have clear physical meanings and rulebased and linguistic information can be incorporated into adaptive fuzzy systems in a systematic way. On the other hand, there exist powerful algorithms for training various neural network models. However, most of the proposed combined architectures are only able to process static inputoutput relationships, i.e. they are not able to process temporal input sequences of arbitrary length. Fuzzy finitestate automata (FFAs) can model dynamical processes whose current state depends on the current input and previous states. Unlike in the case of deterministic finitestate automata (DFAs), FFAs are not in one particular state, rather each state is occupied to some degree defined by a membership function. Based on previous work on encoding DFAs in discretetim...
A Survey on Universal Approximation and Its Limits in Soft Computing Techniques
, 2003
"... This paper deals with the approximation behaviour of soft computing techniques. First, we give a survey of the results of universal approximation theorems achieved so far in various soft computing areas, mainly in fuzzy control and neural networks. We point out that these techniques have common appr ..."
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Cited by 17 (4 self)
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This paper deals with the approximation behaviour of soft computing techniques. First, we give a survey of the results of universal approximation theorems achieved so far in various soft computing areas, mainly in fuzzy control and neural networks. We point out that these techniques have common approximation behaviour in the sense that an arbitrary function of a certain set of functions (usually the set of continuous function, C) can be approximated with arbitrary accuracy # on a compact domain. The drawback of these results is that one needs unbounded numbers of "building blocks" (i.e. fuzzy sets or hidden neurons) to achieve the prescribed # accuracy. If the number of building blocks is restricted, it is proved for some fuzzy systems that the universal approximation property is lost, moreover, the set of controllers with bounded number of rules is nowhere dense in the set of continuous functions. Therefore it is reasonable to make a tradeo# between accuracy and the number of the building blocks, by determining the functional relationship between them. We survey this topic by showing the results achieved so far, and its inherent limitations. We point out that approximation rates, or constructive proofs can only be given if some characteristic of smoothness is known about the approximated function.