Stationary Fuzzy Fokker–Planck Learning and Stochastic Fuzzy Filtering

The application of nonlinear optimization to the estimation of fuzzy model parameters is well known. To do the reverse of this, the concept of stationary fuzzy Fokker-Planck learning (SFFPL) is introduced, i.e., SFFPL applies the fuzzy modeling technique in nonlinear optimization problems. SFFPL is based on the fuzzy approximation of the stationary cumulative distribution function of a stochastic search process associated with the nonlinear optimization problem. A carefully designed algorithm is suggested for SFFPL to locate the optimum point. This paper also considers the variational Bayes (VB)-based inference of a stochastic fuzzy filter whose consequents, as well as antecedents, are random variables. The problem of VB inference of stochastic antecedents, because of the nonlinearity of the likelihood function, is analytically intractable. The SFFPL algorithm for high-dimensional nonlinear optimization that does not require the derivative of the objective function can be used to numerically solve the stochastic fuzzy filtering problem.