Constructing Rule-Based Models Using the Belief Functions Framework

We study a new approach to regression analysis. We propose a new rule-based regression model using the theoretical framework of belief functions. For this purpose we use the recently proposed Evidential c-means (ECM) to derive rule-based models solely from data. ECM allocates, for each object, a mass of belief to any subsets of possible clusters, which allows to gain a deeper insight on the data while being robust with respect to outliers. The proposed rule-based models convey this added information as the examples illustrate.

[1]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[2]  Francesc Esteva,et al.  Review of Triangular norms by E. P. Klement, R. Mesiar and E. Pap. Kluwer Academic Publishers , 2003 .

[3]  Thierry Denoeux Function approximation in the framework of evidence theory: a connectionist approach , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[4]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[5]  J. Ragot,et al.  A Multi-Modeling Strategy based on Belief Function Theory , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[6]  Philippe Smets,et al.  The Combination of Evidence in the Transferable Belief Model , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Philippe Smets,et al.  The Transferable Belief Model for Quantified Belief Representation , 1998 .

[8]  Dov M. Gabbay,et al.  Handbook of defeasible reasoning and uncertainty management systems: volume 2: reasoning with actual and potential contradictions , 1998 .

[9]  Sylvie Le Hégarat-Mascle,et al.  Combination of partially non-distinct beliefs: The cautious-adaptive rule , 2009, Int. J. Approx. Reason..

[10]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[11]  Radko Mesiar,et al.  Triangular Norms , 2000, Trends in Logic.

[12]  Philippe Smets,et al.  Decision making in the TBM: the necessity of the pignistic transformation , 2005, Int. J. Approx. Reason..

[13]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[14]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[15]  Thierry Denoeux,et al.  Nonparametric regression analysis of uncertain and imprecise data using belief functions , 2004, Int. J. Approx. Reason..

[16]  Alessandro Saffiotti,et al.  The Transferable Belief Model , 1991, ECSQARU.

[17]  Bilal M. Ayyub,et al.  Fuzzy regression methods - a comparative assessment , 2001, Fuzzy Sets Syst..

[18]  Thierry Denoeux,et al.  ECM: An evidential version of the fuzzy c , 2008, Pattern Recognit..

[19]  Thierry Denoeux,et al.  RECM: Relational evidential c-means algorithm , 2009, Pattern Recognit. Lett..

[20]  Thierry Denoeux,et al.  Classifier fusion in the Dempster-Shafer framework using optimized t-norm based combination rules , 2011, Int. J. Approx. Reason..

[21]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .