Type-2 fuzzy sets, Markov processes for pattern recognition

二型模糊集, 馬爾科夫過程應用於模式識別

Student thesis: Doctoral Thesis

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  • Jia ZENG

Related Research Unit(s)


Awarding Institution
  • Zhi-Qiang LIU (Supervisor)
Award date15 Feb 2007


This dissertation integrates type-2 fuzzy sets (T2 FSs) with Markov processes (MPs) to handle both randomness and fuzziness in pattern recognition. We view pattern recognition as a labeling problem. First, we use MPs for statistical-structural pattern representation in the labeling problem, which can characterize both statistical and structural uncertainties of patterns in terms of randomness. Furthermore, we use T2 FSs for handling uncertainties such as uncertain class models, uncertain observations, and uncertain structural match. Finally, we integrate the T2 FSs with MPs referred to as the T2 FMPs, which are able to handle both randomness and fuzziness in the labeling problem within a unified framework. In the labeling problem, we assign a set of linguistic labels to a set of sites to explain the observation at all sites. We view the recognition as one of scoring how well a given class model (labels) matches a given observation. Not only can MPs describe statistical information of observations, but also describe the probabilistic interdependence of labels. The maximum a posteriori (MAP) estimation guarantees the single best labeling configuration. We have investigated two MPs, namely Markov random fields (MRFs) and hidden Markov models (HMMs). MRFs haveMarkov property on undirected graphs, which may solve the two-dimensional labeling problem such as handwritten Chinese character recognition. HMMs have Markov property on directed chain graphs, which are suitable for the one-dimensional labeling problem such as speech recognition. However, randomness may not characterize the following fuzziness: (1) Uncertain parameters of the class model because of insufficient and noisy training data, which further lead to uncertain mapping of the model (fuzzy mapping). (2) Uncertain relationship between training and test data due to limited prior information (fuzzy data). (3) Uncertain linguistic labels because the same label may mean different things to different people (fuzzy labeling configuration). In view of this problem, we propose the type-2 fuzzy sets (T2 FSs) to handle both randomness and fuzziness. We may use the primary membership to describe randomness, and use the secondary membership functions to describe the fuzziness of the primary membership. Hence the T2 FS is natural to handle randomness and fuzziness simultaneously, and both uncertainties can be propagated by operations on T2 FSs. Because of fuzziness, we extend the MAP estimation by operations on two T2 FSs, which represent fuzzy likelihood and prior respectively. The integration of MPs with T2 FSs may handle both randomness and fuzziness in the labeling problem. We extend some classical algorithms for MPs by operations on T2 FSs. The classification decision rule is based on the output T2 FS rather than the scalar of the traditional MPs. We applied the proposed approaches to two real-world pattern recognition problems, namely speech recognition and handwritten Chinese character recognition. The experimental results are encouraging, which demonstrate the validity of the proposed approaches.

    Research areas

  • Markov processes, Pattern recognition systems, Fuzzy sets