Continuous HMM with state memberships provided by Takagi-Sugeno fuzzy rule systems (TSFRS)

In this paper we develop an EM based training algorithm for a Takagi-Sugeno fuzzy rule system (TSFRS). Since the training is unsupervised, no target values are needed. The TSFRS models the degree of membership based on a given distribution that can be modified by changing the consequence of the rules or by rule pruning. We use this training algorithm to train a hidden Markov model (HMM) with state memberships provided by TSFRS using a modified Baum-Welch algorithm. This representation has the advantage of being transparent, since one can analyze and modify the rules that form the membership TSFRS.