Generation of partial orders for intervals by means of the slope function

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.