Affiliations: Department of Computer Science, University of Jaén,
E-23071 Jaén, Spain. E-mail: alcala@ujaen.es | Department of Computer Science and Artificial
Intelligence, University of Granada, E-18071 Granada, Spain. E-mail:
{casillas, ocordon, herrera}@decsai.ugr.es
Abstract: The use of Mamdani-type fuzzy rule-based systems (FRBSs) allows us
to deal with the modeling of systems building a linguistic model clearly
interpretable by human beings. However, the accuracy obtained is not sometimes
as good as desired. This fact relates to the restriction imposed when using
linguistic variables, which forces the membership functions considered in each
fuzzy linguistic rule to belong to a common set of them, i.e., to use a global
grid. To solve this problem, in the last few years a new variant has been
proposed working directly with fuzzy variables in the fuzzy rules instead of
linguistic terms, thus ignoring the said restriction. Therefore, these systems,
which are totally equivalent to fuzzy graphs (defined by Zadeh as granular
representations of functional dependencies and relations), do not consider a
global grid and could be named {\it non-grid-oriented} (NGO) FRBSs. Of course,
the main objective of these models is the accuracy of the system instead its
interpretability. Until now, NGO FRBSs have been little considered and
developed in the literature. However, and due to their good accuracy, their use
is increasing thus making necessary a wide analysis on the features and
associated learning methods in the NGO domain. This contribution aims at
analyzing the structure and framework of NGO FRBSs, as well as making a
taxonomy of learning methods considering the constrains imposed on the fuzzy
sets in the generation process. Some automatic learning techniques and methods
proposed in the literature to build these fuzzy graphs will be also reviewed
and analyzed when solving several applications of different nature.
