Hierarchical Fuzzy Hidden Markov Chain for Web Applications

Fuzzy sets, a scheme for handling nonstatistical vague concepts, provide a natural basis for the theory of possibility space. In this paper, on possibility space, a hierarchical generalization of the fuzzy hidden Markov chain (HFHMC) which is named as FHMC is proposed. For the proposed model, three problems which naturally arise in any kind of hidden Markov models (HMMs) are discussed. To solve these problems, generalized Baum-Welch and generalized Viterbi algorithms are formulated; further it is observed that the generalized Viterbi algorithm itself solves the first two problems namely the likelihood of a given observation sequence and finding the most likelihood state sequence, which exhibits that the time complexity involved in the computation of two problems reduces to a single problem. In order to ensure the ease of models use, the proposed model is applied to our institution website and simulation is performed to analyze the accessibility of the website among the users.