ADAPTIVE INFERENCE IN FUZZY KNOWLEDGE NETWORKS

Abstract

Uncertain causal knowledge is stored in fuzzy cognitive maps. (FCHs). 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. An appropriate causal learning law for inductively inferring FCMs from data is the differential Hebbian law, which modifies causal connections by correlating time derivatives of FCM node outputs. FCM nodes represent variable phenomena or fuzzy sets. A FCM node nonlinearly transforms weighted summed inputs into a numerical output. Therein lies the structural similarity of FCMs to neural networks. Unlike expert systems, which are feedforward decision trees with graph search, FCMs are dynamical systems. FCM resonant states are limit cycles. A FCM limit cycle or hidden pattern is a 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. An expert credibility weight wj in [0, 1] is included in this learning process by multiplying the ith expert's augmented FCM connection matrix by wi.