Pattern Analysis and Applications

, Volume 13, Issue 1, pp 85–91

Classification error in Bayes multistage recognition task with fuzzy observations

Theoretical Advances

DOI: 10.1007/s10044-008-0143-9

Cite this article as:
Burduk, R. Pattern Anal Applic (2010) 13: 85. doi:10.1007/s10044-008-0143-9


The paper considers the problem of classification error in multistage pattern recognition. This model of classification is based primarily on the Bayes rule and secondarily on the notion of fuzzy numbers. In adopting a probability-fuzzy model two concepts of hierarchical rules are proposed. In the first approach the local criterion that denote the probabilities of misclassification for particular nodes of a tree is considered. In the second approach the global optimal strategy that minimises the mean probability of misclassification on the whole multistage recognition process is considered. A probability of misclassifications is derived for a multiclass hierarchical classifier under the assumption that the features at different nodes of the tree are class-conditionally statistically independent, and we have fuzzy information on object features instead of exact information. Numerical example of this difference concludes the work.


Hierarchical classifierBayes decision rulesFuzzy observationsProbability of error

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© Springer-Verlag London Limited 2008

Authors and Affiliations

  1. 1.Chair of Systems and Computer NetworksWroclaw University of TechnologyWrocławPoland