A general unified framework for interval pairwise comparison matrices
  Interval Pairwise Comparison Matrices have been widely used to account for
uncertain statements concerning the preferences of decision makers. Several
approaches have been proposed in the literature, such as multiplicative and
fuzzy interval matrices. In this paper, we propose a general unified approach
to Interval Pairwise Comparison Matrices, based on Abelian linearly ordered
groups. In this framework, we generalize some consistency conditions provided
for multiplicative and/or fuzzy interval pairwise comparison matrices and
provide inclusion relations between them. Then, we provide a concept of
distance between intervals that, together with a notion of mean defined over
real continuous Abelian linearly ordered groups, allows us to provide a
consistency index and an indeterminacy index. In this way, by means of suitable
isomorphisms between Abelian linearly ordered groups, we will be able to
compare the inconsistency and the indeterminacy of different kinds of Interval
Pairwise Comparison Matrices, e.g. multiplicative, additive, and fuzzy, on a
unique Cartesian coordinate system.
