Dimension of fuzzy ordered sets

Abstract The notion of a multichain in a fuzzy ordered set is defined. By means of multichains the dimension Fd s ( X , R ) of a fuzzy ordered set is given. The properties of the dimension function are studied. The dimension Fd s Y of a subset Y of a fuzzy set X can be greater than Fd s X . The dimension of the min-product of n fuzzy linearly ordered sets is not greater than n . Every fuzzy ordered set( X , R ) with Fd s X = n , is isomorphic to a section subset of the max-product of n fuzzy linearly ordered sets.