Fuzzy Cognitive Maps: Analysis and Extensions

Fuzzy cognitive map (FCM) [5] was a modification of the cognitive map of Axelrod [1]. FCMs can be used in knowledge representation and inference which are essential to any intelligent system. FCM encodes rules in its networked structure in which all concepts are causally connected. Rules are fired based on a given set of initial conditions and the structure of the FCM. The resulting map pattern represents the causal inference of the FCM. In FCMs, we are able to represent all concepts and arcs (edges) connecting the concepts by symbols or numerical values. Moreover, in such a framework it is possible to handle different types of uncertainties effectively and to combine readily several FCMs into a single FCM that takes the knowledge from different experts into consideration [6]. FCM provides a mechanism for handling causality between events/objects in a more natural fashion. Indeed, FCM is a flexible and realistic representation scheme for dealing with knowledge. This scheme is potentially useful in the development of human-centered systems that require soft-knowledge in the sense that system concepts, their relationships, and the meta-system knowledge can be represented only to a certain degree. In addition, subtle (spatial and temporal) variations in the knowledge base can often result in completely different outcomes or decisions [25]. Many recently developed systems and successful applications have shown that fuzzy cognitive maps represent a promising paradigm for the development of functional intelligent systems [10, 15, 19, 20].