H∞ estimation for fuzzy membership function optimization

Abstract

Given a fuzzy logic system, how can we determine the membership functions that will result in the best performance? If we constrain the membership functions to a specific shape (e.g., triangles or trapezoids) then each membership function can be parameterized by a few variables and the membership optimization problem can be reduced to a parameter optimization problem. The parameter optimization problem can then be formulated as a nonlinear filtering problem. In this paper we solve the nonlinear filtering problem using H 1 state estimation theory. However, the membership functions that result from this approach are not (in general) sum normal. That is, the membership function values do not add up to one at each point in the domain. We therefore modify the H 1 filter with the addition of state constraints so that the resulting membership functions are sum normal. Sum normality may be desirable not only for its intuitive appeal but also for computational reasons in the real time implementation of fuzzy logic systems. The methods proposed in this paper are illustrated on a fuzzy automotive cruise controller and compared to Kalman filtering based optimization.

Cardiomyopathy Detection from Electrocardiogram Features

“…Constrained Kalman filtering can further improve fuzzy system results by optimally constraining the network parameters (Simon, 2002c). H-infinity estimation is another gradient-based method that can be used for fuzzy system training to improve robustness to data errors (Simon, 2005).…”

Biogeography-based optimization of neuro-fuzzy system parameters for diagnosis of cardiac disease

“…Constrained Kalman filtering can further improve fuzzy system results by optimally constraining the network parameters [28]. H-infinity estimation is another gradient-based method that can be used for fuzzy system training to improve robustness to data errors [29].…”

Optimization of multiple input–output fuzzy membership functions using clonal selection algorithm

“…To improve behavior of this parameter optimization problem some methods such as genetic algorithms (GA), self-organizing feature maps (SOFM), tabu search (TS) etc. can be used Bai & Chen, 2008;Bagis ß, 2003;Cerrada, Aguilar, Colina, & Titli, 2005;Chen, Hong, & Tseng, 2009;Cheng & Lui, 1997;Karr, 1991;Lee & Takagi, 1993;Meredith, Karr, & Krishna Kumar, 1992;Sakiroglu & Arslan, 2007;Simon, 2005;Yang and Bose,2006). GA was used by Karr (1991) in determination of membership functions.…”

“…Cerrada et al (2005) proposed an approach permits incorporate the temporal behavior of the system variables into the fuzzy membership functions. Simon (2005) employed H 1 state estimation theory for the membership function parameter optimization. He made some modifications on the H filter with addition of state constraints so that the resulting membership functions are sum normal.…”