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 [Bart Kosko, "Fuzzy Cognitive Maps", International Journal of Man-Machine Studies, 24(1986) 65-75 (first introduction of FCMs): [ http://sipi.usc.edu/~kosko/FCM.pdf] see also [ http://sipi.usc.edu/~kosko/Virtual_Worlds_FCM.pdf] ] .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 [On line calculator and downloadable Java applications for FCM computations: http://www.ochoadeaspuru.com/fuzcogmap/index.php] .

A simple application of FCMs is described in a bookWilliam R. Taylor: " [http://www.americanconfusion.com/?p=122 Lethal American Confusion] (How Bush and the Pacifists Each Failed in the War on Terrorism)", 2006, ISBN 0595406556 (FCM application in chapter 14)] of William R. Taylor, where the war in Afghanistan and Iraq is analyzed. And in Bart Kosko's book "Fuzzy Thinking"Bart Kosko: "Fuzzy Thinking", 1993/1995, ISBN 078688021X (Chapter 12: Adaptive Fuzzy Systems)"] , several Hasse diagrams illustrate the use of FCMs. As an example, one FCM quoted from Rod TaberRod Taber: "Knowledge Processing with Fuzzy Cognitive Maps", Expert Systems with Applications, vol. 2, no. 1, 83-87, 1991 ( [http://de.wikipedia.org/wiki/Bild:FCMdrug520.pngHasse diagram] in German Wikipedia)] 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 Rod Taber, Ronald R. Yager, and Cathy M. Helgason:Quantization Effects on the Equilibrium Behavior of Combined Fuzzy Cognitive Maps, International Journal of Intelligent Systems, vol. 22, 181-202, 2007.]

While applications in social sciences [Costas Neocleous, Christos Schizas, Costas Yenethlis: " [http://www.congreso-info.cu/UserFiles/File/Info/Info2006/Ponencias/271.pdf Fuzzy Cognitive Models in Studying Political Dynamics - The case of the Cyprus problem] "] 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 [Chrysostomos D. Stylios, Voula C. Georgopoulos, Peter P. Groumpos: " [http://med.ee.nd.edu/MED5/PAPERS/067/067.PDF The Use of Fuzzy Cognitive Maps in Modeling Systems] "] of uncertainty and complex processes and systems. Examples:
*In business FCMs can be used for product planning [Antonie Jetter: "Produktplanung im Fuzzy Front End", 2005, ISBN 3835001442] .
*In economics, FCMs support the use of game theory in more complex settings [Vesa A. Niskanen: " [http://www.ijicic.org/fic04-20.pdf Application of Fuzzy Linguistic Cognitive Maps to Prisoner's Dilemma] ", 2005, ICIC International pp. 139-152, ISSN 1349-4198] .
*In project planning FCMs help to analyze the mutual dependencies between project resources.
*In robotics [Marc Böhlen: " [http://www.realtechsupport.org/pdf/SpaceRobotics2000.pdf More Robots in Cages] ", ] 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 [Benjoe A. Juliano, Wylis Bandler: "Tracing Chains-of-Thought (Fuzzy Methods in Cognitive Diagnosis)", Physica-Verlag Heidelberg 1996, ISBN 3790809225] .
*And in expert systems a few or many FCMs can be aggregated into one FCM in order to process estimates of knowledgeable persons [W. B. Vasantha Kandasamy, Florentin Smarandache: " [http://www.gallup.unm.edu/~smarandache/NCMs.pdf Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps] ", 2003, ISBN: 1931233764 (This book is an excellent general introduction to various applications of FCMs.)] . [L. Rodriguez-Repiso, R. Setchi, and J.L. Salmeron. Modelling IT Projects success with Fuzzy Cognitive Maps. Expert Systems with Applications 32(2) pp. 543-559. 2007]

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