Abstract
Fuzzy cognitive maps are studied from statistical standpoint. An analogy between these maps and linear regression and logistic regression models is drawn. Practical examples are also provided.
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References
R. Axelrod, Structure of Decision. The Cognitive Maps of Political Elites (Princeton University Press, Princeton, 1976)
H. Bandemer, W. Näther, Fuzzy Data Analysis (Kluwer, Dordrecht, 1992)
M. Buruzs, M. Hatwágner L.T. Kóczy, Expert-based method of integrated waste management systems for developing fuzzy cognitive map, in Complex System Modelling and Control Through Intelligent Soft Computations. Studies in Fuzziness and Soft Computing, vol. 319, ed. by Q. Zhu, A. Azar (2015), pp. 111–137
J.P. Carvalho, J. Tome, Rule based fuzzy cognitive maps in socio-economic systems, in Proceedings of the IFSA Congress (Lisbon, 2009), pp. 1821–1826
S. Chiu, Fuzzy model identification based on cluster estimation. J. Intell. Fuzzy Syst. 2, 267–278 (1994)
V. Dimitrov, B. Hodge, Social Fuzziology—Study of Fuzziness of Social Complexity (Physica Verlag, Heidelberg, 2002)
D. Freedman, Statistical models: Theory and practice (Cambridge University Press, Cambridge, 2005)
Fuzzy Logic User’s Guide 2018a, Mathworks, 2018, www.mathworks.com/help/pdf_doc/fuzzy/fuzzy.pdf
M. Glykas (ed.), Fuzzy Cognitive Maps (Springer, Heidelberg, 2010)
P. Grzegorzewski, O. Hryniewicz, M. Gil, Soft Methods in Probability. Statistics and Data Analysis (Physica Verlag, Heidelberg, 2002)
M. Hatwagner, V. Niskanen L. Koczy, Behavioral analysis of fuzzy cognitive map models by simulation, in Proceedings of the IFSA ’17 Congress, Otsu, Japan, https://ieeexplore.ieee.org/abstract/document/8023345/
S. Kim, C. Lee, Fuzzy implications of fuzzy cognitive map with emphasis on fuzzy causal relationship and fuzzy partially causal relationship. Fuzzy Sets Syst. 97(3), 303–3013 (1998)
B. Kosko, Fuzzy Engineering (Prentice Hall, Upper Saddle River, New Jersey, 1997)
K.C. Lee, W.J. Lee, O.B. Kwon, J.H. Han, P.I. Yu, Strategic planning simulation based on fuzzy cognitive map knowledge and differential game. Simulation 71(5), 316–327 (1998)
R. Kruse, K. Meyer, Statistics with Vague Data (Reidel, Dordrecht, 1987)
J. Metsämuuronen, Essentials in Research Methods in Human Sciences, Multivariate Analysis (Sage, London, 2017)
J. Metsämuuronen, Essentials in Research Methods in Human Sciences, Advanced Analysis (Sage, London, 2017)
V.A. Niskanen, Application of logistic regression analysis to fuzzy cognitive maps, in Fuzzy Logic Theory and Applications, vol. 2, ed. by L. Zadeh, R. Aliev (World Scientific Publishing, Singapore, 2019)
V.A. Niskanen, Concept map approach to approximate reasoning with fuzzy extended logic, in Fuzzy Technology: Present Applications and Future Technology, Studies in Fuzziness and Soft Computing, vol. 335, ed. by M. Fedrizzi, M. Collan, J. Kacprzyk, (Springer, Heidelberg, 2016), pp. 47–70
J. Novak, Learning, Creating, and Using Knowledge: Concept Maps as Facilitative Tools in Schools and Corporations (Lawrence Erlbaum Associates Inc, New Jersey, 1998)
E. Papageorgiou, E. Stylios, P. Groumpos, Fuzzy cognitive map learning based on nonlinear Hebbian rule, in AI 2003. LNCS (LNAI), vol. 2903, ed. by T. Gedeon, L. Fung (Springer, 2003), pp. 256–268
W. Pedrycz, A. Jastrzebska, W. Homenda, Design of fuzzy cognitive maps for modeling time series. IEEE Transactions of Fuzzy Systems 24(1), 120–130 (2016)
W. Stach, L. Kurgan, W. Pedrycz, Expert-based and computational methods for developing fuzzy cognitive maps, in Fuzzy Cognitive Maps, ed. by M. Glykas (Springer, 2010), pp. 24–41
W. Stach, L.A. Kurgan W. Pedrycz, Numerical and linguistic prediction of time series with the use of fuzzy cognitive maps. IEEE Trans. Fuzzy Syst. 16 (2008)
W. Stach, L. Kurgan, W. Pedrycz, M. Reformat, Genetic learning of fuzzy cognitive maps. Fuzzy Sets Syst. 153, 371–401 (2005)
W. Stach, L. Kurgan, W. Pedrycz, A survey of fuzzy cognitive map learning methods. Issues Soft Comput. Theory Appl., pp. 71–84 (2005)
C. Stylios, P. Groumpos, Modeling complex systems using fuzzy cognitive maps. IEEE Trans. Syst. Man Cybern. Part A 34(1), 155–162 (2004)
F. Wenstøp, Quantitative analysis with linguistic values. Fuzzy Sets Syst. 4, 99–115 (1980)
L. Zadeh, Fuzzy logic = computing with words. IEEE Trans. Fuzzy Syst. 2, 103–111 (1996)
L. Zadeh, Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90(2), 111–127 (1997)
L. Zadeh, From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circ. Syst. 45, 105–119 (1999)
L. Zadeh, Toward a perception-based theory of probabilistic reasoning with imprecise probabilities. J. Stat. Plann. Infer. 105(2), 233–264 (2002)
Acknowledgements
I express my thanks to the distinguished Editors for having this opportunity to be one of the contributors of this book. This article is dedicated to the memory of my mentor and friend, the great Professor Lotfi Zadeh.
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Niskanen, V.A. (2020). Statistical Approach to Fuzzy Cognitive Maps. In: Shahbazova, S., Sugeno, M., Kacprzyk, J. (eds) Recent Developments in Fuzzy Logic and Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol 391. Springer, Cham. https://doi.org/10.1007/978-3-030-38893-5_3
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