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AFS Algebras and Their Representations of Membership Degrees

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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, first we construct some lattices—AFS algebras using sets X and M over an AFS structure (M,τ,X) for the representation of the membership degrees of each sample x ∈ X belonging to the fuzzy concepts in EM. Then the mathematical properties and structures of AFS algebras are exhaustively discussed. Finally, the relations, advantages and drawbacks of various kinds of AFS representations for fuzzy concepts in EM are analyzed. Some results listed without proofs are left for the reader as exercises.

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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 Algebras and Their Representations of Membership Degrees. 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_5

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  • DOI: https://doi.org/10.1007/978-3-642-00402-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00401-8

  • Online ISBN: 978-3-642-00402-5

  • eBook Packages: EngineeringEngineering (R0)

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