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Fuzzy hidden Markov chain with states depending on observation for web applications. (English) Zbl 1400.60094
Summary: This paper provides a novel approach en route to the fuzzy hidden Markov chain to have an additional property namely the observation dependent property. In fuzzy hidden Markov chain the current state depends only on one state that is the immediately preceding state. The newly added property makes the fuzzy hidden Markov chain to depend on two things (1) the immediately preceding state and (2) the immediately preceding observation. The specialism is that though this newly developed fuzzy hidden Markov chain depends on two values the state sequence remains a Markov chain. This paper also solves the three problems evaluation, optimal state sequence and parameter re-estimation for the developed model by giving new algorithms. These algorithms are applied to our institution’s website to know the pattern of the website’s usage.
MSC:
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60A86 Fuzzy probability
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