Towards an Extension of the 2-tuple Linguistic Model to Deal With
  Unbalanced Linguistic Term sets
  In the domain of Computing with words (CW), fuzzy linguistic approaches are
known to be relevant in many decision-making problems. Indeed, they allow us to
model the human reasoning in replacing words, assessments, preferences,
choices, wishes... by ad hoc variables, such as fuzzy sets or more
sophisticated variables.
  This paper focuses on a particular model: Herrera & Martinez' 2-tuple
linguistic model and their approach to deal with unbalanced linguistic term
sets. It is interesting since the computations are accomplished without loss of
information while the results of the decision-making processes always refer to
the initial linguistic term set. They propose a fuzzy partition which
distributes data on the axis by using linguistic hierarchies to manage the
non-uniformity. However, the required input (especially the density around the
terms) taken by their fuzzy partition algorithm may be considered as too much
demanding in a real-world application, since density is not always easy to
determine. Moreover, in some limit cases (especially when two terms are very
closed semantically to each other), the partition doesn't comply with the data
themselves, it isn't close to the reality. Therefore we propose to modify the
required input, in order to offer a simpler and more faithful partition. We
have added an extension to the package jFuzzyLogic and to the corresponding
script language FCL. This extension supports both 2-tuple models: Herrera &
Martinez' and ours. In addition to the partition algorithm, we present two
aggregation algorithms: the arithmetic means and the addition. We also discuss
these kinds of 2-tuple models.
