Virtual Worlds as Fuzzy Cognitive Maps

Abstract

Fuzzy cognitive maps (FCM) can structure virtual worlds that change with time. An FCM links causal events, actors, values, goals, and trends in a fuzzy feedback dynamical system. An FCM lists the fuzzy rules or causal flow paths that relate events. It can guide actors in a virtual world as the actors move through a web of cause and effect and react to events and to other actors. Experts draw FCM causal pictures of the virtual world. They do not write down differential equations to change the virtual world. Complex FCMs can give virtual worlds with “new” or chaotic equilibrium behavior. Simple FCMs give virtual worlds with periodic behavior. They map input states to limit-cycle equilibria. An FCM limit cycle repeats a sequence of events or a chain of actions and responses. Limit cycles can control the steady-state rhythms and patterns in a virtual world. In nested FCMs each causal concept can control its own FCM or fuzzy function approximator. This gives levels of fuzzy systems that can choose goals and causal webs as well as move objects and guide actors in the webs. FCM matrices sum to give a combined FCM virtual world for any number of knowledge sources. Adaptive FCMs change their fuzzy causal web as causal patterns change and as actors act and experts state their causal knowledge. Neural learning laws change the causal rules and the limit cycles. Actors learn new patterns and reinforce old ones. In complex FCMs the user can choose the dynamical structure of the virtual world from a spectrum that ranges from mildly to wildly nonlinear. We use a simple but adaptive FCM to model an undersea virtual world of dolphins, fish, and sharks.