A Dirichlet Process Based Type-1 and Type-2 Fuzzy Modeling for Systematic Confidence Bands Prediction

This paper presents a new methodology for fuzzy logic systems modeling based on the Dirichlet process Gaussian mixture models (DPGMM). The proposed method simultaneously allows for the systematic elicitation of confidence bands as well as the automatic determination of model complexity. This work is new since existing fuzzy model elicitation techniques use ad hoc methods for confidence band estimations, which do not meet the stringent requirements of today's challenging environments where data are sparse, incomplete, and characterized by noise as well as uncertainties. The proposed approach involves an integration of fuzzy and Bayesian topologies and allows for the generation of confidence bands based on both the random and linguistic uncertainties embedded in the data. Additionally, the proposed method provides a “right-first time approach” to fuzzy modeling as it does not require an iterative model complexity determination. In order to see how the proposed framework performs across a variety of challenging data modeling problems, the proposed approach was tested on a nonlinear synthetic dataset as well as two real multidimensional datasets generated by the authors from materials science and bladder cancer studies. Results show that the proposed approach consistently provides better generalization performances than other well-known soft computing modeling frameworks-in some cases, improvements of up to 20% in modeling accuracy were achieved. The proposed method also provides the capability to handle uncertainties via the generation of systematic confidence intervals for informing on model reliability. These results are significant since the generic methodologies developed in this paper should help material scientists as well as clinicians, for example, assess the risks involved in making informed decisions based on model predictions.