Generalized hidden Markov models - Part I: Theoretical frameworks

This is the first paper in a series of two papers describing a novel genera lization of classical hidden Markov models using fuzzy measures and fuzzy i ntegrals, In this paper, we present the theoretical framework for the gener alization and, in the second paper, we describe an application of the gener alized hidden Markov models to handwritten word recognition. The main chara cteristic of the generalization is the relaxation of the usual additivity c onstraint of probability measures. Fuzzy integrals are defined with respect to fuzzy measures, whose kg property is monotonicity with respect to set i nclusion. This property is far weaker than the usual additivity property of probability measures. As a result of the new formulation, the statistical independence assumption of the classical hidden Markov models is relaxed, A n attractive property of this generalization is that the generalized hidden Markov model reduces to the classical hidden Markov model if we used the C hoquet fuzzy integral and probability measures. Another interesting propert y of the generalization is the establishment of a relation between the gene ralized hidden Markov model and the classical nonstationary hidden Markov m odel in which the transitional parameters vary with time.