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215
The Spatial Semantic Hierarchy
 Artificial Intelligence
, 2000
"... The Spatial Semantic Hierarchy is a model of knowledge of largescale space consisting of multiple interacting representations, both qualitative and quantitative. The SSH is inspired by the properties of the human cognitive map, and is intended to serve both as a model of the human cognitive map and ..."
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Cited by 239 (28 self)
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The Spatial Semantic Hierarchy is a model of knowledge of largescale space consisting of multiple interacting representations, both qualitative and quantitative. The SSH is inspired by the properties of the human cognitive map, and is intended to serve both as a model of the human cognitive map and as a method for robot exploration and mapbuilding. The multiple levels of the SSH express states of partial knowledge, and thus enable the human or robotic agent to deal robustly with uncertainty during both learning and problemsolving. The control level represents useful patterns of sensorimotor interaction with the world in the form of trajectoryfollowing and hillclimbing control laws leading to locally distinctive states. Local geometric maps in local frames of reference can be constructed at the control level to serve as observers for control laws in particular neighborhoods. The causal level abstracts continuous behavior among distinctive states into a discrete model ...
Fuzzy logic controllers are universal approximators
 IEEE Trans. on SMC
, 1995
"... AbstractIn this paper, we consider a fundamental theoretical question, Why does fuzzy control have such good performance for a wide variety of practical problems?. We try to answer this fundamental question by proving that for each fixed fuzzy logic belonging to a wide class of fuzzy logics, and fo ..."
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Cited by 80 (7 self)
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AbstractIn this paper, we consider a fundamental theoretical question, Why does fuzzy control have such good performance for a wide variety of practical problems?. We try to answer this fundamental question by proving that for each fixed fuzzy logic belonging to a wide class of fuzzy logics, and for each fixed type of membership function belonging to a wide class of membership functions, the fuzzy logic control systems using these two and any method of defdcation are capable of approximating any real continuous function on a compact set to arbitrary accuracy. On the other hand, this result can be viewed as an existence theorem of an optimal fuzzy logic control system for a wide variety of problems. 1 I.
Dynamic Control of Genetic Algorithms using Fuzzy Logic Techniques
 PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON GENETIC ALGORITHMS
, 1993
"... This paper proposes using fuzzy logic techniques to dynamically control parameter settings of genetic algorithms (GAs). We describe the Dynamic Parametric GA: a GA that uses a fuzzy knowledgebased system to control GA parameters. We then introduce a technique for automatically designing and t ..."
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Cited by 53 (0 self)
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This paper proposes using fuzzy logic techniques to dynamically control parameter settings of genetic algorithms (GAs). We describe the Dynamic Parametric GA: a GA that uses a fuzzy knowledgebased system to control GA parameters. We then introduce a technique for automatically designing and tuning the fuzzy knowledgebase system using GAs. Results from initial experiments show a performance improvement over a simple static GA. One Dynamic Parametric GA system designed by our automatic method demonstrated improvement on an application not included in the design phase, which may indicate the general applicabilityof the Dynamic Parametric GA to a wide range of applications.
A new methodology of extraction, optimization and application of crisp and fuzzy logical rules
 IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2001
"... A new methodology of extraction, optimization, and application of sets of logical rules is described. Neural networks are used for initial rule extraction, local, or global minimization procedures for optimization, and Gaussian uncertainties of measurements are assumed during application of logical ..."
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Cited by 49 (23 self)
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A new methodology of extraction, optimization, and application of sets of logical rules is described. Neural networks are used for initial rule extraction, local, or global minimization procedures for optimization, and Gaussian uncertainties of measurements are assumed during application of logical rules. Algorithms for extraction of logical rules from data with realvalued features require determination of linguistic variables or membership functions. Contextdependent membership functions for crisp and fuzzy linguistic variables are introduced and methods of their determination described. Several neural and machine learning methods of logical rule extraction generating initial rules are described, based on constrained multilayer perceptron, networks with localized transfer functions or on separability criteria for determination of linguistic variables. A tradeoff between accuracy/simplicity is explored at the rule extraction stage and between rejection/error level at the optimization stage. Gaussian uncertainties of measurements are assumed during application of crisp logical rules, leading to “soft trapezoidal” membership functions and allowing to optimize the linguistic variables using gradient procedures. Numerous applications of this methodology to benchmark and reallife problems are reported and very simple crisp logical rules for many datasets provided.
Neural Networks in Designing Fuzzy Systems for Real World Applications”, Fuzz y
 University of Sydney
, 1995
"... AbstractA special multilayer perceptron architecture known as FuNe I is successfully used for generating fuzzy systems for a number of real world applications. The FuNe I trained with supervised learning can be used to extract fuzzy rules from a given representative input/output data set. Furthermo ..."
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Cited by 46 (8 self)
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AbstractA special multilayer perceptron architecture known as FuNe I is successfully used for generating fuzzy systems for a number of real world applications. The FuNe I trained with supervised learning can be used to extract fuzzy rules from a given representative input/output data set. Furthermore, optimization of the knowledge base is possible including the tuning of membership functions. The new method employed to identify the rule relevant nodes before the rules are extracted makes FuNe I suitable for applications with large number of inputs. Some of the real world applicationsinareas of state identi cation and image classi cation show encouraging results in a shorter development time. Expert knowledge is not compulsory but can be included in the automatically extracted knowledge base. The generated fuzzy system can be implemented in hardware very easily. A exible prototype board is developed with a FPGA chip in order to run applications with up to 128 inputs and 4 outputs in realtime (1.25 million rules per second).
Labeling RAAM
 Connection Science
, 1994
"... In this paper we propose an extension of the Recursive AutoAssociative Memory (RAAM) by Pollack. This extension, the Labeling RAAM (LRAAM), is able to encode labeled graphs with cycles by representing pointers explicitly. A theoretical analysis of the constraints imposed on the weights by the learn ..."
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Cited by 44 (10 self)
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In this paper we propose an extension of the Recursive AutoAssociative Memory (RAAM) by Pollack. This extension, the Labeling RAAM (LRAAM), is able to encode labeled graphs with cycles by representing pointers explicitly. A theoretical analysis of the constraints imposed on the weights by the learning task under the hypothesis of perfect learning and linear output units is presented. Cycles and confluent pointers result to be particularly effective in imposing constraints on the weights. Some technical problems encountered in the RAAM, such as the termination problem in the learning and decoding processes, are solved more naturally in the LRAAM framework. The representations developed for the pointers seem to be robust to recurrent decoding along a cycle. Data encoded in a LRAAM can be accessed by pointer as well as by content. The direct access by content can be achieved by transforming the encoder network of the LRAAM in a Bidirectional Associative Memory (BAM). Different access pro...
A Hierarchy of Qualitative Representations for Space
 In Working papers of the Tenth International Workshop on Qualitative Reasoning about Physical Systems (QR96
, 1996
"... . Research in Qualitative Reasoning builds and uses discrete symbolic models of the continuous world. Inference methods such as qualitative simulation are grounded in the theory of ordinary differential equations. We argue here that cognitive mapping  building and using symbolic models of the ..."
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Cited by 35 (7 self)
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. Research in Qualitative Reasoning builds and uses discrete symbolic models of the continuous world. Inference methods such as qualitative simulation are grounded in the theory of ordinary differential equations. We argue here that cognitive mapping  building and using symbolic models of the largescale spatial environment  is a highly appropriate domain for qualitative reasoning research. We describe the Spatial Semantic Hierarchy (SSH), a set of distinct representations for space, each with its own ontology, each with its own mathematical foundation, and each abstracted from the levels below it. At the control level, the robot and its environment are modeled as a continuous dynamical system, whose stable equilibrium points are abstracted to a discrete set of "distinctive states." Trajectories linking these states can be abstracted to actions, giving a discrete causal graph level of representation for the state space. Depending on the properties of the actions, th...
Survey of Neural Transfer Functions
 Neural Computing Surveys
, 1999
"... The choice of transfer functions may strongly influence complexity and performance of neural networks. Although sigmoidal transfer functions are the most common there is no apriorireason why models based on such functions should always provide optimal decision borders. A large number of alternative ..."
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Cited by 35 (19 self)
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The choice of transfer functions may strongly influence complexity and performance of neural networks. Although sigmoidal transfer functions are the most common there is no apriorireason why models based on such functions should always provide optimal decision borders. A large number of alternative transfer functions has been described in the literature. A taxonomy of activation and output functions is proposed, and advantages of various nonlocal and local neural transfer functions are discussed. Several lessknown types of transfer functions and new combinations of activation/output functions are described. Universal transfer functions, parametrized to change from localized to delocalized type, are of greatest interest. Other types of neural transfer functions discussed here include functions with activations based on nonEuclidean distance measures, bicentral functions, formed from products or linear combinations of pairs of sigmoids, and extensions of such functions making rotations...
SelfOrganizing and Genetic Algorithms for an Automatic Design of Fuzzy Control and Decision Systems
 In Proc. EUFIT'93
, 1993
"... An automatic design method is proposed for fuzzy control and decision/diagnosis systems. This method extends traditional fuzzy systems by a learning ability without changing the fuzzy rule framework. The fuzzy rules and linguistic variables are extracted from a referential data set by a selforganiz ..."
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Cited by 34 (6 self)
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An automatic design method is proposed for fuzzy control and decision/diagnosis systems. This method extends traditional fuzzy systems by a learning ability without changing the fuzzy rule framework. The fuzzy rules and linguistic variables are extracted from a referential data set by a selforganizing process. A genetic algorithm is used to find optimal input/output membership functions.