|Title||On Extending Fuzzy Preorders to Sets and Their Corresponding Strict Orders|
|Publication Type||Book Chapter|
|Year of Publication||2018|
|Authors||Esteva F, Godo L|
|Book Title||The Mathematics of the Uncertain|
In this paper we first consider the problem of extending a fuzzy (weak) preorder on a set W to a fuzzy relation (preorder) on subsets of W, and consider different possibilities using different forms of quantification. For each of them we propose possible definitions of corresponding indistinguishability and strict preorder relations associated to the initial preorder, both on W and on its power set P(W). We compare them and we study conditions under which the strict relation is transitive.
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