Recently Hidden Markov Models (HMMs) and Stochastic grammar models have been extensively employed in various fields like computational biology, speech recognition, gesture recognition and text processing with the problems being modelled using classical probability measures. Fuzzy measure is an extension to the classical measure theory with promising applications in various areas. Some generalized HMMs have been developed with fuzzy measures for the speech recognition problem. The well known algorithms used for HMMs are thereby shown to execute faster. In this article, we discuss the classical and fuzzy measure formulation of HMMs, followed by applications in speech recognition using fuzzy measures. We also indicate the possible scope for their application to Bioinformatics.