Nested FCM:

• each node in turn can control its own simple FCM

• FCM nesting extends to any number of fuzzy sets for the inputs. A concept can divide into smaller fuzzy sets or subconcepts. The edges or rules link the sets.

• complex actions such as walking emerge from networks of simple reflexes.

Augmented FCM:

• includes the union of the causal concepts for all the actors and the environment in the virtual world

• if a FCM does not include a concept then those rows and columns are all zero.

• the sum of the augmented (zero-padded) FCM matrices for each actor forms the virtual world:

Complex FCM:

• user can choose the dynamical structure of the virtual world from a spectrum that ranges from mildly to wildly nonlinear

Why virtual world is a dynamical system:

• it changes with time as the user/actor moves through it

• actors cause events to happen as they move in a virtual world

• feedback causality between actors and virtual world makes up a complex dynamical system that can model events

Fuzzy dynamical world:

• events occur and concept hold only to some degree

• events cause one another to some degree

• in a virtual world the concept nodes can stand for events. The causal edges state fuzzy rules or causal flows between concepts

FCM system:

• the FCM system turns each picture into a matrix of fuzzy rule weights. The system weights and adds the FCM matrices to combine any number of causal pictures.

• this makes it easy to add or delete actors or to change the background of a virtual world or to combine virtual worlds

Positive and negative edge rules:

• the sign (+ or —) of an edge stands for causal increase or decrease.

• the positive edge rule states that a survival threat increases runaway.

Calculation of state vector:

The system nonlinearly transforms the weighted input to each node Ci:

Sigmoid function: