Abstract
First, we outline the group-based trajectory models for longitudinal data; second, we briefly describe the concept of propensity scores based on these models; third, we give a new perspective of propensity scores in fuzzy sets; fourth, we apply operations of fuzzy sets to propensity scores; fifth, we generalize propensity scores to trajectories based on fuzzy and possibilistic clusterings.
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References
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algoritms. Plenum Press, New York (1981)
Dubois, D., et al.: Probability-Possibility Transformations, Triangular Fuzzy Sets, and Probabilistic Inequalities. Reliable Computing 10, 273–297 (2004)
Garcia-Laencina, P.J., et al.: Pattern classification with missing data: a review. Neural Computing and Applications 19, 263–282 (2010)
Krishnapuram, R., et al.: A possibilistic approach to clustering. IEEE Trans. on Fuzzy Systems 1, 98–110 (1993)
Krishnapuram, R., et al.: The possibilistic C-Means algorithm: insights and recommendations. IEEE Trans. on Fuzzy Systems 4, 385–393 (1996)
Liu, X.: Entropy, distance measure and similarity measure of fuzzy sets and their relations. Fuzzy Sets and Systems 52, 305–318 (1992)
Liu, X. et al.: Measuring individual propensity to follow a developmental trajectory. University of Montreal, Technical report (2011)
Nagin, D.S.: Analyzing Developmental Trajectories: Semi-Parametric, Group-Based Approach. Psychological Methods 4, 139–177 (1999)
Nagin, D.S.: Group-based Modeling of Development. Harvard University Press, Cambridge (2005)
Rubin, D.B.: Inference and missing data (with discussion). Biometrika 63, 581–592 (1976)
Zadeh, L.A.: Fuzzy Sets. Inf. Control 8, 338–353 (1965)
Zadeh, L.A.: Fuzzy Set Theoretic Interpretation Linguistic Hedges. J. of Cybernetics 2, 4–34 (1972)
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© 2011 Springer-Verlag Berlin Heidelberg
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Liu, X., Tremblay, R.E., Cote, S., Carbonneau, R. (2011). Linking Developmental Propensity Score to Fuzzy Sets: A New Perspective, Applications and Generalizations. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_41
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DOI: https://doi.org/10.1007/978-3-642-22833-9_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22832-2
Online ISBN: 978-3-642-22833-9
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