A. Fuzzy Causal Networks

Abstract

Abstract—In this paper, we first propose a general framework for fuzzy causal networks (FCNs). Then, we study the dynamics and convergence of such general FCNs. We prove that any general FCN with constant weight matrix converges to a limit cycle or a static state, or the trajectory of the FCN is not repetitive. We also prove that under certain conditions a discrete state general FCN converges to its limit cycle or static state in ( ) steps, where is the number of vertices of the FCN. This is in striking contrast with the exponential running time 2, which is accepted widely for classic FCNs. Index Terms—Fuzzy causal network (FCN), fuzzy cognitive map, fuzzy system, inference, intelligent system

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