Nonstandard fuzzy sets (Q1821099)

Given a set X, the lattice \(F(X,^*[0,1])\) of the nonstandard fuzzy subsets of X is considered, i.e. the L-subsets with L equal to the unit interval \({}^*[0,1]\) of a nonstandard model of analysis. To show the appropriateness of such a concept, two examples of vague concepts are given. The first example is ''positive divergence'' for functions and the second is ''vagueness'' for fuzzy sets. These concepts are representable by suitable nonstandard fuzzy sets while they are not representable by Zadeh's fuzzy sets.