Fuzzy Cognitive Map

Hasse Diagram s are used to visualize FCMs. Spreadsheet s or tables are used to map FCMs into Matrix es for further computationOn 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: '' 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 ( Hasse 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}). The 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 sciencesCostas Neocleous, Christos Schizas, Costas Yenethlis: '' 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 modelsChrysostomos D. Stylios, Voula C. Georgopoulos, Peter P. Groumpos: '' 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 planningAntonie Jetter: ''Produktplanung im Fuzzy Front End'', 2005, ISBN 3835001442.

In economics, FCMs support the use of Game Theory in more complex settingsVesa A. Niskanen: '' 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 roboticsMarc Böhlen: '' 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 lessonsBenjoe A. Juliano, Wylis Bandler: ''Tracing Chains-of-Thought (Fuzzy Methods in Cognitive Diagnosis)'', Physica-Verlag Heidelberg 1996, ISBN 3790809225.

And in Expert System s a few or many FCMs can be aggregated into one FCM in order to process estimates of knowledgeable personsW. 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.).

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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Fuzzy Cognitive Map