Type-2 fuzzy hidden Markov models and their application to speech recognition

This paper presents an extension of hidden Markov models (HMMs) based on the type-2 (T2) fuzzy set (FS) referred to as type-2 fuzzy HMMs (T2 FHMMs). Membership functions (MFs) of T2 FSs are three-dimensional, and this new third dimension offers additional degrees of freedom to evaluate the HMMs fuzziness. Therefore, T2 FHMMs are able to handle both random and fuzzy uncertainties existing universally in the sequential data. We derive the T2 fuzzy forward-backward algorithm and Viterbi algorithm using T2 FS operations. In order to investigate the effectiveness of T2 FHMMs, we apply them to phoneme classification and recognition on the TIMIT speech database. Experimental results show that T2 FHMMs can effectively handle noise and dialect uncertainties in speech signals besides a better classification performance than the classical HMMs.