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Fuzzy Information and Engineering pp 280–289Cite as

Normal Distribution Fuzzy Sets

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Part of the book series: Advances in Soft Computing ((AINSC,volume 40))

Abstract

Owing to the theory of intuitionistic fuzzy sets for fuzzy sets generalization extends the membership degree from a single value in [0, 1] to a subinterval in [0, 1], it brings forward two questions: 1. Whether all the values in the subinterval have the same probabilities as the membership degree or not? 2. If the probabilities in the subinterval are different, which kind of distribution will they be? In this paper, a method for expressing an intuitionistic fuzzy set by a series of normal distribution functions has been presented according to the investigation of vote model. The theory of normal distribution fuzzy sets is established. This theory solve the problems existing in intuitionistic fuzzy sets, the probability distribution of membership degree in [0, 1] can be clearly recognized. The notion of inclusion, union, intersection, and complement extending to such sets and the properties of normal distribution fuzzy sets are discussed in detail. The relationship among fuzzy sets, intuitionistic fuzzy sets and normal distribution fuzzy sets is specified.

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Author information

Authors and Affiliations

  1. College of Computer Science & Technology, Huazhong University of Science and Technology, Wuhan 430074, China

    Zehua Lv & Wenhai Li

  2. School of Software Engineering, Huazhong University of Science and Technology, Wuhan 430074, China

    Chuanbo Chen

Authors
  1. Zehua Lv
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  2. Chuanbo Chen
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  3. Wenhai Li
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Editor information

Bing-Yuan Cao

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© 2007 Springer-Verlag Berlin Heidelberg

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Lv, Z., Chen, C., Li, W. (2007). Normal Distribution Fuzzy Sets. In: Cao, BY. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71441-5_31

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  • DOI: https://doi.org/10.1007/978-3-540-71441-5_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71440-8

  • Online ISBN: 978-3-540-71441-5

  • eBook Packages: EngineeringEngineering (R0)

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