Dominance, potential optimality, imprecise information, and hierarchical structure in multi-criteria analysis

Incorporating the imprecision of both weights and values into multi-attribute value theory brings us some computational difficulties in evaluating alternatives to be considered. For instance, we involve treating a non-linear programming problem because of non-linear forms of objectives or constraints to represent inner product forms of imprecisely known weights and values. In this paper, we thus develop a technique to translate such non-linear programming problems into ordinary linear programming equivalents. Note that there exits an earlier method similar to those developed in the present paper. However, that method has a limitation where it is assumed that there exists at least one alternative that has the only value of unity to be maximal in the corresponding attribute. This limitation is removed in the present article and, further, an extension is made to handle hierarchical structures.