Fuzzy Cognitive Maps - is a model of reality that works by using cause and effect relationships.

Structure - each node in FCM represents a concept. Each arc (C_i, C_j) is directed as well as weighted, and represents causal link between concepts, showing how concept C_i causes concept C_j.

Creating a picture can both create a structure for the talk, but also provide new insights on the subject.

FCMs are fuzzy because arbitrary weights can be assigned to the causal links and the beginning values of the concepts of a FCM. These weights are a number between 0 (or -1) and 1.

The value of the concept nodes in a FCM is either within the boundaries [-1, ... , 1] or [0, ... , 1].

The values of the relationships between two concepts are always in the interval [-1, ... , 1].

Simple variations of FCMs use only the trivalent values [-1, 0, 1] for the relations. This simplifies the creation of the FCM: it's easier to pinpoint the sign of the relationship and solve problems if greater detail of the output is wanted.

FCM Inference Algorithm

1. Definition of the initial vector A that corresponds to theelements-concepts identified by experts’ suggestions andavailable knowledge.

2. Multiply the initial vector A with the matrix W defined by experts

3. The resultant vector A at time step k is updated usingfunction threshold ‘ f ’.

4. This new vector is considered as an initial vector in the next iteration.

5. Steps 2–4 are repeated until epsilon (where describes the minimum error difference among thesubsequent concepts).

Matrix Vector Product

FCM results - high values of the concepts mean that they are valid to a high degree, low values correspond with low degrees of validity.

The Extended FCMs utilize a modified version of equation:

where delay_ij is the delay on that causal link. Extended FCMs also have the possibility for the weights of the network not to be the same for each different value of C.