α-Discounting Multi-Criteria Decision Making (α-D MCDM)

In this paper we introduce a new method called \alpha-Discounting Multi-Criteria Decision Making (\alpha-D MCDM), which is an aletrnative and extension of Saaty's Analytical Hierarchy Process (AHP). It works for any set of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. \alpha-D MCDM is then generalized to a set of preferences that can be transformed into a system of linear and/or non-linear equations and/or inequalities. Many consistent, weak inconsistent, and strong inconsistent examples are given.