Distances in Agents' Preferences Graphs in Decision Problems

Many of the methods proposed so far for solving the problems of the distribution of homogeneous indivisible goods widely described in the literature use allocation rules. In such an approach, appropriate functions are defined which assign exactly one solution to any allocation problem. The allocation of homogeneous indivisible goods is one of the types of problems that can be viewed through the lens of orders generated by permutations. Elements of the classes of such orders, which are identified with the preferences of decision-makers expressed through partial orders, enable other innovative approaches leading to a set of not necessarily single element optimal allocations. To this end, a matrix of distances between decision variants was constructed which in turn is basis for an IMFOS algorithm returning a set of optimal variants. The solutions introduced in the paper are not limited to the allocation problems, and can be used in various types of decision problems. In addition, the constructed matrix can be the basis for selecting optimal variants using the proposed IMFOS algorithm as well as many other well-known MCDM methods.