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AFS Fuzzy Clustering Analysis

  • Chapter
Axiomatic Fuzzy Set Theory and Its Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 244))

Abstract

In this chapter, we apply the AFS theory to propose an elementary algorithm of fuzzy clustering. In the proposed approach, each cluster is interpreted by taking advantage of the semantics captured by the AFS logic. Within the framework of AFS theory, we develop new techniques of feature selection, concept categorization and characteristic description (i.e.,the characteristic description of an object or a group of objects using the fuzzy concepts) which are often encountered in tasks of machine learning and pattern recognition. The elementary fuzzy clustering algorithm is evolved to three more elaborate fuzzy clustering techniques by incorporating new techniques of feature selection, concept categorization and characteristic description. We show that they are simpler and produce more interpretable results when contrasted with some existing techniques. Several benchmark data and the evaluation data of 30 companies are considered to evaluate the effectiveness of the proposed AFS fuzzy clustering algorithms. We provide a detailed comparative analysis in which we compare the obtained results with those produced by some “conventional” methods such as FCM, k-means, and some newer algorithms including a two-level SOM-based clustering algorithm. The proposed algorithms can be applied to the data sets with mixed features such as sub-preference relations and even those including descriptions of human intuitive judgment. We show that the flexibility of the approach comes from the fact that the distance function and the class number need not be given beforehand. These two facets offers a far more higher flexible and contribute to a powerful framework for representing human knowledge and studying intelligent systems encountered in real world applications.

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Authors
  1. Xiaodong Liu
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  2. Witold Pedrycz
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Liu, X., Pedrycz, W. (2009). AFS Fuzzy Clustering Analysis. In: Axiomatic Fuzzy Set Theory and Its Applications. Studies in Fuzziness and Soft Computing, vol 244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00402-5_9

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  • DOI: https://doi.org/10.1007/978-3-642-00402-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00401-8

  • Online ISBN: 978-3-642-00402-5

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