Solving multi-criteria decision making with incomplete linguistic preference relations

When there are n criteria or alternatives in a decision matrix, a pairwise comparison methodology of analytic hierarchy process (AHP) with the time of n(n ? 1)/2 is frequently used to select, evaluate or rank the neighboring alternatives. But while the number of criteria or comparison level increase, the efficiency and consistency of a decision matrix decrease. To solve such problems, this study therefore uses horizontal, vertical and oblique pairwise comparisons algorithm to construct multi-criteria decision making with incomplete linguistic preference relations model (InLinPreRa). The use of pairwise comparisons will not produce the inconsistency, even allows every decision maker to choose an explicit criterion or alternative for index unrestrictedly. When there are n criteria, only n ? 1 pairwise comparisons need to be carried out, then one can rest on incomplete linguistic preference relations to obtain the priority value of alternative for the decision maker’s reference. The decision making assessment model that constructed by this study can be extensively applied to every field of decision science and serves as the reference basis for the future research.