Characterization of fuzzy subsets by Galois

RNDr. Ľubomír Antoni, PhD.

Abstract

We present the one-to-one correspondence between the set of all fuzzy subsets and the set of all Galois connections. The essential correspondences are built with the help of a-cuts, which represent fuzzy subsets by classical sets. Moreover, we present a relationship between strong fuzzy negations in the lattices and Galois connections. The various extensions of fuzzy subsets from the point of view of nestedness and negations are recalled.