Assessing priority weights from subsets of pairwise comparisons in multiple criteria optimization problems

Using a set covering concept we explore the possibility and flexibility of selecting a subset of all possible pairs of comparisons to assess priority weights of the decision criteria. Different techniques offer different priority weights with different properties. They are, however, interrelated when special subsets such as basic coverings, elementary cycles and complete covering are considered. This paper provides a framework for unifying existing assessment methods, and offers some fundamental theorems which reveal the intricate relationships among the methods over the subsets.