Fuzzy cognitive map

A Fuzzy cognitive map is a cognitive map within which the relations between the elements (e.g. concepts, events, project resources) of a "mental landscape" can be used to compute the "strength of impact" of these elements. The theory behind that computation is fuzzy logic. Fuzzy cognitive maps are signed fuzzy digraphs. They may look at first blush like Hasse diagrams but they are not. Spreadsheets or tables are used to map FCMs into Matrixes for further computation.

A simple application of FCMs is described in a book of William R. Taylor, where the war in Afghanistan and Iraq is analyzed. And in Bart Kosko's book Fuzzy Thinking, several Hasse diagrams illustrate the use of FCMs. As an example, one FCM quoted from Rod Taber describes 11 factors of the American cocaine market and the relations between these factors. For computations, Taylor uses pentavalent logic (scalar values out of {-1,-0.5,0,+0.5,+1}). That particular map of Taber uses trivalent logic (scalar values out of {-1,0,+1}). Taber et al. also illustrate the dynamics of map fusion and give a theorem on the convergence of combination in a related article

While applications in social sciences  introduced FCMs to the public, they are used in a much wider range of applications, which all have to deal with creating and using models of uncertainty and complex processes and systems. Examples:
 * In business FCMs can be used for product planning.
 * In economics, FCMs support the use of game theory in more complex settings.
 * In project planning FCMs help to analyze the mutual dependencies between project resources.
 * In robotics FCMs support machines to develop fuzzy models of their environments and to use these models to make crisp decisions.
 * In computer assisted learning FCMs enable computers to check, whether students understand their lessons.
 * And in expert systems a few or many FCMs can be aggregated into one FCM in order to process estimates of knowledgeable persons.