Lattice-valued F-transforms as interior operators of L-fuzzy pretopological spaces

Abstract

The focus is on two spaces with a weaker structure than that of a fuzzy topology. The first one is a fuzzy pretopological space, and the second one is a space with an L-fuzzy partition. For a fuzzy pretopological space, we prove that it can be determined by a Čech interior operator and that the latter can be represented by a reflexive fuzzy relation. For a space with an L-fuzzy partition, we show that a lattice-valued F↓-transform is a strong Čech-Alexandrov fuzzy interior operator. Conversely, we found conditions that guarantee that a given L-fuzzy pretopology determines the L-fuzzy partition and the corresponding F↓-transform operator.