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Theory Based on Interval-Valued Level Cut Sets of Zadeh Fuzzy Sets

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Fuzzy Information and Engineering Volume 2

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 62))

Abstract

In this paper, the concepts of interval-valued level cut sets on Zadeh fuzzy sets are presented and new decomposition theorems of Zadeh fuzzy sets based on new cut sets are established. Firstly, four interval-valued level cut sets on Zadeh fuzzy sets are introduced, which are generalizations of the normal cut sets on Zadeh fuzzy sets and have the same properties as that of the normal cut sets on Zadeh fuzzy sets. Secondly, based on these new cut sets, the new decomposition theorems of Zadeh fuzzy sets are established. It is pointed that each kind of interval-valued level cut sets corresponds to two decomposition theorems. Thus eight decomposition theorems are obtained. Finally, the definitions of \(\bar{L}\)-inverse order nested sets and \(\bar{L}\)-order nested sets are introduced and we established eight new representation theorems on Zadeh fuzzy sets by using the concept of new nested sets.

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Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, Dalian University of Technology, Dalian, 116024, P.R. China

    Xue-hai Yuan, Hong-xing Li & Kai-biao Sun

Authors
  1. Xue-hai Yuan
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  2. Hong-xing Li
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  3. Kai-biao Sun
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Editor information

Editors and Affiliations

  1. Guangzhou University, China

    Bingyuan Cao

  2. Chongqing University of Science and Technology, Chongqing, PR China

    Tai-Fu Li

  3. Hainan Normal University, Hainan, PR China

    Cheng-Yi Zhang

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© 2009 Springer-Verlag Berlin Heidelberg

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Yuan, Xh., Li, Hx., Sun, Kb. (2009). Theory Based on Interval-Valued Level Cut Sets of Zadeh Fuzzy Sets. In: Cao, B., Li, TF., Zhang, CY. (eds) Fuzzy Information and Engineering Volume 2. Advances in Intelligent and Soft Computing, vol 62. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03664-4_55

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  • DOI: https://doi.org/10.1007/978-3-642-03664-4_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03663-7

  • Online ISBN: 978-3-642-03664-4

  • eBook Packages: EngineeringEngineering (R0)

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