9. Designing and Training Relational Fuzzy Cognitive Maps

This chapter deals with certain aspects of the design of fuzzy cognitive maps, which operations are based not on a set of causal rules but on mathematically defined relationships between the model key concepts. In such a model, which can be called a relational fuzzy cognitive map, the key concepts are described by fuzzy numbers, and the relationships between concepts take the form of specially shaped fuzzy relations. As a result, the operation of the model is described mathematically by the system of special equations operating on fuzzy numbers and relations. This approach introduces formal and technical difficulties but on the other hand, it allows to apply certain automation of the process of creating and modifying the relational model of a fuzzy cognitive map. It also enables detachment from the rigidly defined linguistic values in relation to their abstract equivalents, which number can be easily changed depending on the current needs of the modeling process. The chapter describes the results of work up until today by authors of design of fuzzy relational models of cognitive maps.