The design of cognitive maps: A study in synergy of granular computing and evolutionary optimization

Cognitive maps and fuzzy cognitive maps offer interesting and transparent modeling capabilities by functioning at a level of conceptual entities (nodes) and their relationships expressed either at the qualitative level of excitatory/inhibitory relationships or being further numerically quantified as encountered in fuzzy cognitive maps. While there has been a vast array of conceptual enhancements, a relatively less attention has been paid to the design of the maps especially when dealing with an algorithmic way of forming the map. The objective of this study is to offer a design strategy in which starting with experimental evidence in the form of numeric data, those data are transformed into a finite and small number of concepts (nodes) of the map and afterwards the connections of the map are estimated. We show that techniques of Granular Computing, especially fuzzy clustering are effectively used to form concepts (nodes) of well-articulated semantics. In the sequel, we show the use of global optimization in the form of Particle Swarm Optimization (PSO) to carry out calibration of the connections of the interrelationships between the nodes of the map. Numeric examples are concerned with the representation of time series and their visualization in the form of fuzzy cognitive maps. Further interpretation of the maps is also discussed.