Linear orders and semiorders close to an interval order
A partial order is linear if for every x,y,z,w \(x<y\) and \(z<w\to x<w\) or \(z<y\). An interval order is a semiorder if \(x<y\) and \(y<z\to x<w\) or \(w<z\). The semiorder (linear order) P' is close to a given finite partial order P if it minimizes the cardinality of the symmetric difference \(P\Delta\) P'. There is proved one, rather elementary, theorem on semiorders close to a given interval order. (Since the terminology is about 75\% of the paper, it is impossible to quote this result in a short review.)
scientific article; zbMATH DE number 3849288