  The seven-valued logic considered in this paper naturally arises within the
rough set framework, allowing to distinguish vagueness due to imprecision from
ambiguity due to coarseness. Recently, we discussed its utility for reasoning
about data describing multi-attribute classification of objects. We also showed
that this logic contains, as a particular case, the celebrated Belnap
four-valued logic. Here, we present how the seven-valued logic, as well as the
other logics that derive from it, can be used to represent preferences in the
domain of Multiple Criteria Decision Aiding (MCDA). In particular, we propose
new forms of outranking and value function preference models that aggregate
multiple criteria taking into account imperfect preference information. We
demonstrate that our approach effectively addresses common challenges in
preference modeling for MCDA, such as uncertainty, imprecision, and
ill-determination of performances and preferences. To this end, we present a
specific procedure to construct a seven-valued preference relation and use it
to define recommendations that consider robustness concerns by utilizing
multiple outranking or value functions representing the decision maker s
preferences. Moreover, we discuss the main properties of the proposed
seven-valued preference structure and compare it with current approaches in
MCDA, such as ordinal regression, robust ordinal regression, stochastic
multiattribute acceptability analysis, stochastic ordinal regression, and so
on. We illustrate and discuss the application of our approach using a didactic
example. Finally, we propose directions for future research and potential
applications of the proposed methodology.
