Hidden patterns in combined and adaptive knowledge networks

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 time-series 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 output-correlation 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 time-varying 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 o f 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 This research was supported by the Air Force Office of Scientific Research (AFOSR F49620-86-C0070) and the Advanced Research Projects Agency of the Department of Defense under ARPA Order No. 5794. Address Correspondence to Bart Kosko, Department of Electrical Engineering--Systems, Signal and Information Processing Institute, University of Southern California, Los Angeles, CA 90089-0272. International Journal of Approximate Reasoning 1988; 2:377-393 © 1988 Elsevier Science Publishing Co., Inc. 52 Vanderbilt Ave., New York, NY 10017 0888-613X/88/$3.50 377