Interval-valued level cut sets of fuzzy set

Xue-hai Yuan (), Hong-xing Li and Kai-biao Sun
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Xue-hai Yuan: Dalian University of Technology
Hong-xing Li: Dalian University of Technology
Kai-biao Sun: Dalian University of Technology

Fuzzy Information and Engineering, 2011, vol. 3, issue 2, 209-222

Abstract: 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.

Keywords: Fuzzy sets; Interval-valued level cut sets; Decomposition theorems; Representation theorems (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s12543-011-0078-5

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