$\alpha$-Discounting Multi-Criteria Decision Making ($\alpha$-D MCDM)
  In this book we introduce a new procedure called \alpha-Discounting Method
for Multi-Criteria Decision Making (\alpha-D MCDM), which is as an alternative
and extension of Saaty Analytical Hierarchy Process (AHP). It works for any
number 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
afterwards generalized to a set of preferences that can be transformed into a
system of linear and or non-linear homogeneous and or non-homogeneous equations
and or inequalities. The general idea of \alpha-D MCDM is to assign non-null
positive parameters \alpha_1, \alpha_2, and so on \alpha_p to the coefficients
in the right-hand side of each preference that diminish or increase them in
order to transform the above linear homogeneous system of equations which has
only the null-solution, into a system having a particular non-null solution.
After finding the general solution of this system, the principles used to
assign particular values to all parameters \alpha is the second important part
of \alpha-D, yet to be deeper investigated in the future. In the current book
we propose the Fairness Principle, i.e. each coefficient should be discounted
with the same percentage (we think this is fair: not making any favoritism or
unfairness to any coefficient), but the reader can propose other principles.
For consistent decision-making problems with pairwise comparisons,
\alpha-Discounting Method together with the Fairness Principle give the same
result as AHP. But for weak inconsistent decision-making problem,
\alpha-Discounting together with the Fairness Principle give a different result
from AHP. Many consistent, weak inconsistent, and strong inconsistent examples
are given in this book.
