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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[1]. 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[2].

A simple application of FCMs is described in a book[3] of William R. Taylor, where the war in Afghanistan and Iraq is analyzed. And in Bart Kosko's book Fuzzy Thinking[4], several Hasse diagrams illustrate the use of FCMs. As an example, one FCM quoted from Rod Taber[5] 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 [6]

While applications in social sciences[3][4][5][7] 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[8] of uncertainty and complex processes and systems. Examples:

  • In business FCMs can be used for product planning[9].
  • In economics, FCMs support the use of game theory in more complex settings[10].
  • In project planning FCMs help to analyze the mutual dependencies between project resources.
  • In robotics[4][11] 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[12].
  • And in expert systems[5] a few or many FCMs can be aggregated into one FCM in order to process estimates of knowledgeable persons[13].


References Edit

  1. Bart Kosko, Fuzzy Cognitive Maps, International Journal of Man-Machine Studies, 24(1986) 65-75 (first introduction of FCMs): [] see also []
  2. On line calculator and downloadable Java applications for FCM computations:
  3. 3.0 3.1 William R. Taylor: Lethal American Confusion (How Bush and the Pacifists Each Failed in the War on Terrorism), 2006, ISBN 0595406556 (FCM application in chapter 14)
  4. 4.0 4.1 4.2 Bart Kosko: Fuzzy Thinking, 1993/1995, ISBN 078688021X (Chapter 12: Adaptive Fuzzy Systems)
  5. 5.0 5.1 5.2 Rod Taber: Knowledge Processing with Fuzzy Cognitive Maps, Expert Systems with Applications, vol. 2, no. 1, 83-87, 1991 (Hasse diagram in German Wikipedia)
  6. 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.
  7. Costas Neocleous, Christos Schizas, Costas Yenethlis: Fuzzy Cognitive Models in Studying Political Dynamics - The case of the Cyprus problem
  8. Chrysostomos D. Stylios, Voula C. Georgopoulos, Peter P. Groumpos: The Use of Fuzzy Cognitive Maps in Modeling Systems
  9. Antonie Jetter: Produktplanung im Fuzzy Front End, 2005, ISBN 3835001442
  10. Vesa A. Niskanen: Application of Fuzzy Linguistic Cognitive Maps to Prisoner's Dilemma, 2005, ICIC International pp. 139-152, ISSN 1349-4198
  11. Marc Böhlen: More Robots in Cages,
  12. Benjoe A. Juliano, Wylis Bandler: Tracing Chains-of-Thought (Fuzzy Methods in Cognitive Diagnosis), Physica-Verlag Heidelberg 1996, ISBN 3790809225
  13. W. B. Vasantha Kandasamy, Florentin Smarandache: Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps, 2003, ISBN: 1931233764 (This book is an excellent general introduction to various applications of FCMs.)
  14. 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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