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Axiomatic Fuzzy Set Theory and Its Applications pp 111–166Cite as

AFS Logic, AFS Structure and Coherence Membership Functions

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

Abstract

In this chapter, we start with an introduction to EI algebra and AFS structure. Then the coherence membership functions of fuzzy concepts for AFS fuzzy logic for the AFS structure are proposed and a new framework of determining coherence membership functions is developed by taking both fuzziness (subjective imprecision) and randomness (objective uncertainty) into account. Singpurwalla’s measure of the fuzzy events in a probability space has been applied to explore the proposed framework. Finally, the consistency, stability, efficiency and practicability of the proposed methodology are illustrated and studied via various numeric experiments. The investigations in this chapter open a door to explore the deep statistic properties of fuzzy sets. In this sense, they may offer further insights as to the to a role of natural languages in probability theory.

The aim of this chapter is to develop a practical and effective framework supporting the development of membership functions of fuzzy concepts based on semantics and statistics completed with regard to fuzzy data. We show that the investigations concur with the main results of the Singpurwalla’s theory [44].

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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 Logic, AFS Structure and Coherence Membership Functions. 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_4

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  • DOI: https://doi.org/10.1007/978-3-642-00402-5_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00401-8

  • Online ISBN: 978-3-642-00402-5

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