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Hidden Patterns in Combined and Adaptive Knowledge Networks
 International Journal of Approximate Reasoning
, 1988
"... Uncertain causal knowledge is stored in fuzzy cognitive maps (FCMs). FCMs are fuzzy signed digraphs with feedback. The sign (+ or) of FCM edges indicates causal increase or causal decrease. The fuzzy degree of causality is indicated by a number in [ 1, 1]. FCMs learn by modifying their causal conn ..."
Abstract

Cited by 38 (2 self)
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Uncertain causal knowledge is stored in fuzzy cognitive maps (FCMs). FCMs are fuzzy signed digraphs with feedback. The sign (+ or) of FCM edges indicates causal increase or causal decrease. The fuzzy degree of causality is indicated by a number in [ 1, 1]. FCMs learn by modifying their causal connections in sign and magnitude, structurally analogous to the way in which neural networks learn. An appropriate causal learning law for inductively inferring FCMs from timeseries data is the differential Hebbian law, which modifies causal connections by correlating time derivatives of FCM node outputs. The differential Hebbian law contrasts with Hebbian outputcorrelation learning laws of adaptive neural networks. FCM nodes represent variable phenomena or fuzzy sets. An FCM node nonlinearly transforms weighted summed inputs into numerical output, again in analogy to a model neuron. Unlike expert systems, which are feedforward search trees, FCMs are nonlinear dynamical systems. FCM resonant states are limit cycles, or timevarying patterns. An FCM limit cycle or hidden pattern is an FCM inference. Experts construct FCMs by drawing causal pictures or digraphs. The corresponding connection matrices are used for inferencing. By additively combining augmented connection matrices, any number of FCMs can be naturally combined into a single knowledge network. The credibility wi in [0, 1] of the ith expert is included in this learning process by multiplying the ith expert's augmented FCM connection matrix by w i. Combining connection matrices is a simple type of adaptive inference. In general, connection matrices are modified by an unsupervised learning law, such as the
Neurofuzzy modeling based on deterministic annealing approach
 Int. J. Appl. Math. Comput. Sci
, 2005
"... This paper introduces a new learning algorithm for artificial neural networks, based on a fuzzy inference system ANBLIR. It is a computationally effective neurofuzzy system with parametrized fuzzy sets in the consequent parts of fuzzy ifthen rules, which uses a conjunctive as well as a logical int ..."
Abstract

Cited by 1 (1 self)
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This paper introduces a new learning algorithm for artificial neural networks, based on a fuzzy inference system ANBLIR. It is a computationally effective neurofuzzy system with parametrized fuzzy sets in the consequent parts of fuzzy ifthen rules, which uses a conjunctive as well as a logical interpretation of those rules. In the original approach, the estimation of unknown system parameters was made by means of a combination of both gradient and leastsquares methods. The novelty of the learning algorithm consists in the application of a deterministic annealing optimization method. It leads to an improvement in the neurofuzzy modelling performance. To show the validity of the introduced method, two examples of application concerning chaotic time series prediction and system identification problems are provided.