Incomplete Ordinal Information in Value Tree Analysis

In value tree analysis, additive value functions are used to model alternatives' overall values. Diculties in complete evaluation of alternatives' attribute-specic values (scores) and attributes' relative importance have spurred research on the modeling of incomplete preference information. This thesis shows how incomplete ordinal information, captured as ordinal information where a set of rankings is associated with a set of attributes or alternatives, can be used in preference modeling. The thesis develops a model for computation of non-dominated alternatives and decision recommendations in a setting where incomplete ordinal information about (i) attributes' relative importance, and/or (ii) alternatives' values with regard to any subsets of attributes, is present. Computational challenges arising from possible non-convexity of the corresponding feasible region of attribute weights and scores are addressed by mixed integer linear programming formulation. Linearity allows also other forms of incomplete information to be used with incomplete ordinal information and thus extends applicability of other preference modeling methods. Incomplete ordinal information can be a useful extension to preference modeling possibilities, including for example settings where: (i) preliminary results or initial screening of alternatives are needed without exhaustive numerical evaluation, (ii) evaluation of intangible attributes is dicult, (iii) decision makers have diculties to agree on numerical values in group settings, (iv) interpretation of attribute weights' numerical values is dicult, (v) information about al-ternatives' properties is based on classication and thus by nature incomplete ordinal, or (vi) resources do not suce for exhaustive pairwise comparisons of attributes' relative importance.