Fuzzy cognitive map

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Rod Tabers FCM depicting eleven factors of the American drug market

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 matrices for further computation.[2][3][4]

A collection of papers with applications in various disciplines is presented in the book "Fuzzy Cognitive Maps: Advances in Theory, Methodologies, Applications and Tools[5] edited by Michael Glykas and prefaced by Bart Kosko. A simple application of FCMs is described in a book[6] of William R. Taylor, where the war in Afghanistan and Iraq is analyzed. And in Bart Kosko's book Fuzzy Thinking,[7] several Hasse diagrams illustrate the use of FCMs. As an example, one FCM quoted from Rod Taber[8] 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 [9]

While applications in social sciences[6][7][8][10] 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[11] of uncertainty and complex processes and systems. Examples:

  • In business FCMs can be used for product planning.[12]
  • In economics, FCMs support the use of game theory in more complex settings.[13]
  • In project planning FCMs help to analyze the mutual dependencies between project resources.
  • In robotics[7][14] 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.[15]
  • In expert systems[8] a few or many FCMs can be aggregated into one FCM in order to process estimates of knowledgeable persons.[16]
  • In IT project management, a FCM-based methodology helps to success modelling.[17]

FCMappers[18] - an international online community for the analysis and the visualization of fuzzy cognitive maps offer support for starting with FCM and also provide a MS-Excel based tool that is able to check and analyse FCMs. The output is saved as Pajek file and can be visualized within 3rd party software like Pajek, Visone,... . They also offer to adapt the software to specific research needs. On their webpage you also will find a linklist for interesting scientific articles, related software, institutes, people and projects. The FCMappers have about one thousand registered members worldwide.

Additional FCM software tools, such as Mental Modeler,[19][20] have recently been developed as a decision-support tool for use in social science research, collaborative decision-making, and natural resource planning.


  1. ^ Bart Kosko, Fuzzy Cognitive Maps, International Journal of Man-Machine Studies, 24(1986) 65-75 (first introduction of FCMs): [1] see also [2]
  2. ^ FCMapper - Excel based FCM analysis and visualization tool: http://www.FCMappers.net/joomla/index.php?option=com_content&view=article&id=52&Itemid=53
  3. ^ On line calculator and downloadable Java applications for FCM computations: http://www.ochoadeaspuru.com/fuzcogmap/index.php
  4. ^ Java standalone library for FCM computations: http://jfcm.megadix.it/
  5. ^ Michael Glykas, Fuzzy Cognitive Maps: Advances in Theories, Methodologies, Applications and Tools, Springer, 2010, ISBN 978-3-642-03219-6. http://www.springerlink.com/content/978-3-642-03219-6/#section=777335&page=1&locus=19
  6. ^ a b William R. Taylor: Lethal American Confusion[dead link] (How Bush and the Pacifists Each Failed in the War on Terrorism), 2006, ISBN 0-595-40655-6 (FCM application in chapter 14)
  7. ^ a b c Bart Kosko: Fuzzy Thinking, 1993/1995, ISBN 0-7868-8021-X (Chapter 12: Adaptive Fuzzy Systems)
  8. ^ a b c Rod Taber: Knowledge Processing with Fuzzy Cognitive Maps, Expert Systems with Applications, vol. 2, no. 1, 83-87, 1991 (Hasse diagram in German Wikipedia)
  9. ^ 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.
  10. ^ Costas Neocleous, Christos Schizas, Costas Yenethlis: Fuzzy Cognitive Models in Studying Political Dynamics - The case of the Cyprus problem[dead link]
  11. ^ Chrysostomos D. Stylios, Voula C. Georgopoulos, Peter P. Groumpos: The Use of Fuzzy Cognitive Maps in Modeling Systems[dead link]
  12. ^ Antonie Jetter: Produktplanung im Fuzzy Front End, 2005, ISBN 3-8350-0144-2
  13. ^ Vesa A. Niskanen: Application of Fuzzy Linguistic Cognitive Maps to Prisoner's Dilemma[dead link], 2005, ICIC International pp. 139-152, ISSN 1349-4198
  14. ^ Marc Böhlen: More Robots in Cages,
  15. ^ Benjoe A. Juliano, Wylis Bandler: Tracing Chains-of-Thought (Fuzzy Methods in Cognitive Diagnosis), Physica-Verlag Heidelberg 1996, ISBN 3-7908-0922-5
  16. ^ W. B. Vasantha Kandasamy, Florentin Smarandache: Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps, 2003, ISBN 1-931233-76-4
  17. ^ 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.
  18. ^ FCMappers - international community for fuzzy cognitive mapping: http://www.FCMappers.net/
  19. ^ Gray, S. Gray, S., Cox, L., and Henly-Shepard, S. 2013 Mental modeler: A fuzzy-logic cognitive mapping modeling tool for adaptive environmental management. Proceedings of the 46th International Conference on Complex Systems. 963-973. http://www.computer.org/csdl/proceedings/hicss/2013/4892/00/4892a965.pdf
  20. ^ http://www.mentalmodeler.com/

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