10Duality in Fuzzy Sets
The concept of 
‐level sets of fuzzy sets is an important tool to study the properties of fuzzy sets and their applications. In this chapter, the 
‐level sets will treated as the upper 
‐level sets. In other words, we are going to introduce a new concept of so‐called lower 
‐level sets, which can also be regarded as the dual concept of upper 
‐level sets.
10.1 Lower and Upper Level Sets
Let 
be a fuzzy set in 
with membership function 
. For 
, the 
‐level set of that may be ...
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