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Hierarchical Fuzzy Hidden Markov Chain for Web Applications

Author

Listed:
  • R. Sujatha

    (Department of Mathematics, SSN College of Engineering, Old Mahabalipuram Road, Chennai, Tamil Nadu, India)

  • T. M. Rajalaxmi

    (Department of Mathematics, SSN College of Engineering, Old Mahabalipuram Road, Chennai, Tamil Nadu, India)

Abstract

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.

Suggested Citation

  • R. Sujatha & T. M. Rajalaxmi, 2016. "Hierarchical Fuzzy Hidden Markov Chain for Web Applications," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 83-118, January.
    • Handle: RePEc:wsi:ijitdm:v:15:y:2016:i:01:n:s0219622015500376
    DOI: 10.1142/S0219622015500376
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    References listed on IDEAS

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    1. Gang Kou & Chunwei Lou, 2012. "Multiple factor hierarchical clustering algorithm for large scale web page and search engine clickstream data," Annals of Operations Research, Springer, vol. 197(1), pages 123-134, August.
    2. A. G. López-Herrera & E. Herrera-Viedma & M. J. Cobo & M. A. Martínez & Gang Kou & Yong Shi, 2012. "A Conceptual Snapshot Of The First Decade (2002–2011) Of The International Journal Of Information Technology & Decision Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 247-270.
    3. Daji Ergu & Gang Kou, 2012. "Questionnaire design improvement and missing item scores estimation for rapid and efficient decision making," Annals of Operations Research, Springer, vol. 197(1), pages 5-23, August.
    4. R. Sujatha & T. M. Rajalaxmi & B. Praba, 2013. "Fuzzy Hidden Markov Chain For Web Applications," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 813-835.
    5. Luciano Stefanini, 2008. "A generalization of Hukuhara difference for interval and fuzzy arithmetic," Working Papers 0801, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
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