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AFS Fuzzy Rough Sets

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Axiomatic Fuzzy Set Theory and Its Applications

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

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Abstract

In this chapter, in order to describe the linguistically represented concepts coming from data available in a certain information system, the concept of fuzzy rough sets are redefined and further studied in the setting of the Axiomatic Fuzzy Set (AFS) theory. These concepts will be referred to as AFS fuzzy rough sets [32]. Compared with the “conventional” fuzzy rough sets, the advantages of AFS fuzzy rough sets are twofold. They can be directly applied to data analysis present in any information system without resorting to the details concerning the choice of the implication φ, t-norm and a similarity relation S. Furthermore such rough approximations of fuzzy concepts come with a well-defined semantics and therefore offer a sound interpretation.

The underlying objective of this chapter is to demonstrate that the AFS rough sets constructed for fuzzy sets form their meaningful approximations which are endowed by the underlying semantics. At the same time, the AFS rough sets become directly reflective of the available data.

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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 Rough Sets. 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_6

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  • DOI: https://doi.org/10.1007/978-3-642-00402-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00401-8

  • Online ISBN: 978-3-642-00402-5

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