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Interval-valued level cut sets of fuzzy set

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Fuzzy Information and Engineering

Abstract

The connections between Zadeh fuzzy set and three-valued fuzzy set are established in this paper. The concepts of interval-valued level cut sets on Zadeh fuzzy set are presented and new decomposition theorems and representation theorems of Zadeh fuzzy set are established based on new cut sets. Firstly, four interval-valued level cut sets on Zadeh fuzzy set are defined as three-valued fuzzy sets and it is shown that the interval-valued level cut sets of Zadeh fuzzy set are generalizations of normal cut sets on Zadeh fuzzy set, and have the same properties as those of normal cut sets of Zadeh fuzzy set. Secondly, the new decomposition theorems are established based on these new cut sets. It is pointed out that each kind of interval-valued level cut sets corresponds to two decomposition theorems. Thus eight decomposition theorems are obtained. Finally, the definitions of three-valued inverse order nested sets and three-valued order nested sets are presented with eight representation theorems based on new nested sets.

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Authors and Affiliations

  1. Faculty of Electronic Information and Electrical 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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Correspondence to Xue-hai Yuan.

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Yuan, Xh., Li, Hx. & Sun, Kb. Interval-valued level cut sets of fuzzy set. Fuzzy Inf. Eng. 3, 209–222 (2011). https://doi.org/10.1007/s12543-011-0078-5

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  • DOI: https://doi.org/10.1007/s12543-011-0078-5

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