Fuzzy Alexandrov Topologies Associated to Fuzzy Interval Orders
Gianni Bosi *
DEAMS, Universit`a di Trieste, via Universit`a 1, 34123 Trieste, Italy
Chiaramaria Panozzo
DEM, Universit`a di Brescia, Contrada Santa Chiara 50, 25122 Brescia, Italy
Magal`ı Ernestine Zuanon
DEM, Universit`a di Brescia, Contrada Santa Chiara 50, 25122 Brescia, Italy
*Author to whom correspondence should be addressed.
Abstract
We characterize the fuzzy T0 - Alexandrov topologies on a crisp set X, which are associated to fuzzy interval orders R on X. In this way, we generalize a well known result by Rabinovitch (1978), according to which a crisp partial order is a crisp interval order if and only if the family of all the strict upper sections of the partial order is nested.
Keywords: Fuzzy Alexandrov topology, fuzzy partial order, T0 separation axiom.