Fuzzy numbers used in mathematical programming in the form of interval coefficient, characterize the uncertainty resulting from imprecise, uncertain and incomplete data. And intervals are cut-sets of fuzzy numbers. Since interval ordering is undertaken prior to studying the comparability of intervals, the problem of ordering intervals is crucial for many applications. We introduce a new general parameterized relation between intervals and study the conditions under which it is a partial order, in order to generalize several classical partial orders with the help of the so-called slope function.