Artículos

Cognitive Maps: an Overview and their Application for Student Modeling

Mapas Cognitivos: un Perfil y su Aplicación al Modelado del Estudiante

Alejandro Peña^1,2,3, Humberto Sossa³ and Agustin Gutiérrez³

WOLNM¹, UPIICSA² & CIC³ – National Polytechnic Institute^2,3
Pattern Recognition Laboratory^2,3
31 Julio 1859, # 1099–B, Leyes Reforma, 09310,
Ciudad de México, D. F, México
+52–55–5694–0916

apenaa@ipn.mx, hsossa@cic.ipn.mx, atornes@cic.ipn.mx

Article received on April 18, 2006; accepted on January 08, 2007

Abstract

In this paper we state how Cognitive Maps can be used to model causal phenomena. In addition, we show the application of the Cognitive Maps to the field of the Student Modeling. Conceptually speaking, Cognitive Maps set and simulate the systems dynamics based upon qualitative knowledge. A Cognitive Map is a tool that gives away the entities of the issue of study. Moreover, Cognitive Maps bring out the causal phenomena as cause–effect relationships between concepts. According to the relationships, a topology and a workflow of causal effects is designed. Cognitive Maps aim to predict the evolution of a model through simulation. During the process are achieved causal inferences that estimate the variation on the state of the concepts. The simulation breaks down when the concept values reach a fixed point, a pattern of states or a chaotic region in the search space. Wherefore, in this paper we depict the underlying concepts for Causal Modeling by means of Cognitive Maps. In addition, three versions of Cognitive Maps are outlined. Besides to reveal their mathematical baseline, we illustrate their application through the development of a case of study focus on Student Model.

Keywords: Cognitive Maps, Causal–effect relationships, Concepts, Causal inference, and Student Model.

Resumen

En este artículo se establece como usar los Mapas Cognitivos para modelar fenómenos causales. Además, mostramos su aplicación en el Modelado del Estudiante. Conceptualmente hablando, los Mapas Cognitivos definen y simulan la dinámica de sistemas por medio de conocimiento cualitativo. Un Mapa Cognitivo es una herramienta que revela las entidades del objeto de estudio. Así mismo, los Mapas Cognitivos expresan el fenómeno causal como relaciones causa–efecto entre conceptos. De acuerdo con las relaciones, una topología y un flujo de efectos causales es diseñada. Los Mapas Cognitivos buscan predecir la evolución del modelo mediante simulación. Durante el proceso se realizan inferencias que estiman la variación del estado de los conceptos. La simulación termina cuando los valores de los conceptos arriban a punto fijo, a un patrón de estados, o a una región de caos en el espacio de búsqueda. Por tanto, en este artículo se definen los conceptos base para el modelado causal a través de Mapas Cognitivos. También se presentan tres versiones de Mapas Cognitivos. Además se expresa la base matemática y se ilustra su aplicación en el desarrollo de un Modelo del Estudiante.

Palabras clave: Mapas Cognitivos, Relaciones Causales, Conceptos, Inferencia Causal, y Modelo del Estudiante.

DESCARGA ARTÍCULO EN FORMATO PDF

Acknowledgments

First author states that this work was inspired in a special way for his Father, his brother Jesus and his Helper as part of the projects of World Outreach Light to the Nations Ministries (WOLNM). Also this work was supported by grants: CONACYT–SEP C0146805/747, CONACYT 182329, COFAA DEBEC/651/2006, COTEPABE PL–22–07 and Microsoft Mexico.

References

1. Axelrod, R., Structure of Decision: The Cognitive Maps of Political Elites. Princeton, 1976.        [ Links ]

2. Aguilar, J., A Survey about Fuzzy Cognitive Maps Papers. Int. J. of Computational Cognition, V. 3, No. 2, June, 2003.        [ Links ]

3. Aguilar, J., Dynamic Random Fuzzy Cognitive Maps. Iberoameric J. of Computation and Systems, V. 4, No. 2, April, 2004, 260–271.        [ Links ]

4. Carvalho, J.P., Rule Base–based Cognitive Maps: Qualitative Dynamic Systems Modeling and Simulation. PhD Thesis, Lisboa Technical University, Portugal, October, 2001, (in Portuguese).        [ Links ]

5. Chaib–draa, B., Causal Maps: Theory, Implementation, and Practical Applications in Multiagent Environments. J. IEEE Transactions on Knowledge and Data Engineering, V. 14, No. 6, November, 2002.        [ Links ]

6. Chin, D.N., Empirical Evaluation of User Models and User–Adapted Systems. Int. J. of User Modeling and User–Adapted Interaction, Kluwer Academic Publishers, 2001, 181–194.        [ Links ]

7. Dickerson, J., and B. Kosko, "Virtual Worlds in Fuzzy Cognitive Maps". In Fuzzy Engineering, edited by B., Kosko, Prentice Hall, NJ, 1997.        [ Links ]

8. Eden, C.J., Thinking in Organizations. London: Macmillan, 1979.        [ Links ]

9. Forrester, J.W., Principles of Systems. Waltham, MA: Pegasus Communications, 1968.        [ Links ]

10. Kelly, G. A., The Psychology of Personal Constructs. Norton, 1955.        [ Links ]

11. Klein, J.L., and D.F. Cooper, Cognitive Maps Decision Markers in a Complex Game. J. of Operational Research Soc., 2, 1982, 377–393.        [ Links ]

12. Kosko, B., Fuzzy Cognitive Maps. Int. J. of Man–Machine Studies, V. 24, 1986, 65–75.        [ Links ]

13. Koulouriotis, D.E., I.E. Diakoulakis, D.M. Emiris, E.N. Antonidakis and I.A. Kaliakatsos, Efficiently Modeling and Controlling Complex Dynamic Systems Using Evolutionary Fuzzy Cognitive Maps. Int. J. of Computational Cognition, V. 1, No. 2, 2003, 41–65.        [ Links ]

14. Leont'ev, A., Activity, Consciousness and Personality. Englewood Cliffs, NJ. Prentice Hall, 1978.        [ Links ]

15. Miguelena, F., Scientific Fundaments of the Models. National Polytechnic Institute Press, Mexico, 2000, (in Spanish).        [ Links ]

16. Mohr, S., Software Design for a Fuzzy Cognitive Map Modeling Tool. 66.698 Master's Project, Rensselaer Polytechnic Institute, 1997, URL: http://www.users.voicenet.com/~smohr/fcm_white.html        [ Links ]

17. Montazemi, A.R., and D.W. Conrath, The Use of Cognitive Mapping for Information Requirements Analysis. MIS, 1986, 45–56.        [ Links ]

18. Nakamura, K., S. Iwai and T. Sawaragi, Decision Support Using Causation Knowledge Base, J. IEEE Transactions on Systems, Man and Cybernetics, (12), 1982, 765–777.        [ Links ]

19. Noriega, P.C., Agent Mediated Auctions. The Fish market Metaphor. PhD Dissertation, Barcelona University, Science College, Bellaterra, December, 1997.        [ Links ]

20. Parenthöen, M., J. Tisseay and T. Morineau, "Believe decision for virtual actors". Paper presented at IEEE International conference on Systems, Man and Cybernetics. Hammamet, Tunes, October, 6–9, 2002.        [ Links ]

21. Peña, A. and F. Gutiérrez, "Adaptive Learning through Cognitive Maps", in E–Learn 2004, World Conference on E–Learning in Corporate, Government, Healthcare, & Higher Education, Washington, DC, USA. November, 1–5, 2004, ISBN: 1–880094–54–1.        [ Links ]

22. Peña, A. and J.S. Sossa, Using Cognitive Maps to Develop a Student Model, in Proc. Iberamia 2004, Puebla, México, November 2004.        [ Links ]

23. Peña, A., Collaborative Student Modeling by Cognitive Maps. DFMA 2005, 1st International Conference Distributed Frameworks for Multimedia Applications, Edited by IEEE, French Chapter, Besançon, France February 2005^a, pp. 160–167.        [ Links ]

24. Peña, A., J.S. Sossa, and F. Gutiérrez, Negotiated Learning by Fuzzy Cognitive Maps, WBE 05, 4th International Conference Web–Based Education, IASTED, Grindelwald, Switzerland, February 2005^a, pp. 590–595.        [ Links ]

25. Peña, A., J.S. Sossa, and F. Gutiérrez, Knowledge and Reasoning Supported by Cognitive Maps. MICAI'05, 4Th Mexican International Conference on Artificial Intelligence, Springer Lecture Notes in Artificial Intelligence, Mty. México, November 2005^b, pp. 41–50.        [ Links ]

26. Peña, A., J.S. Sossa, and F. Gutiérrez, Web–Services based Ontology Agent. 2^nd International Conference Distributed Frameworks for Multimedia Applications, Edited by IEEE, Malaysia Chapter. Univeristy Sains Malaysia, Penang, Malasia, May 2006.        [ Links ]

27. Wellman, M. P., Inference in Cognitive Maps. J. of Mathematics & Computers in Simulation, 36, 1994.        [ Links ]

28. Zhang, W.R., Soundness and Completeness of 4–Valued Bipolar Logic, J. Multi Valued Logic and Soft Computing, v. 9, 2003, 241–256.        [ Links ]