9Gradual Elements and Gradual Sets
Let 
be a (crisp) subset of 
. The concept of an element in 
is well known by writing 
. Suppose that 
is a fuzzy set in 
. The main focus of this chapter is to consider the elements of fuzzy set 
. The gradual elements will play the role to be regarded as the elements of 
.
The concepts of gradual elements and gradual sets were introduced by Dubois and Prade [29,30] and Fortin et al. [37], which were inspired by Goetschel [41] and Herencia and Lamata [47]. The gradual element is a function from 
into , and the gradual set is a set‐valued function from into the ...
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