Transparent Fuzzy/Neuro-fuzzy Modelling - Computational Intelligence in Time Series Forecasting - page 273

x The fuzzy clustering is usually used to discover the substructures in the
product space of the available observations, where each cluster defines a
fuzzy region in which the system can be approximated locally by a
corresponding submodel. The location and the parameters of the submodels
are derived from the clusters of the data. By applying cluster validity
measures (Bezdek and Pal, 1998; Gath and Geva, 1989) such as Xie-
Beni's index (Xie and Beni, 1991) or compatible cluster merging
(Kaymak and Babuška, 1995); (Setnes and Kaymak, 1998) and (Setnes,
1999), an appropriate number of clusters can be found. Alternatively, Yao
et al. (2000) have proposed an entropy-based simple fuzzy clustering
algorithm where the number of clusters is automatically determined by the
clustering algorithm itself. In the recent publications of Panchariya et al.
(2003a, 2003b, 2004a, 2004b) a distance-based simple clustering algorithm
has been developed that uses an almost similar idea for the determination
of the number of clusters.
Step 3: Initial Fuzzy Model
x For a rule-based fuzzy model derived from the fuzzy partition matrix and
the cluster prototypes, the rules themselves, the membership functions, and
other model parameters, such as rules consequent parameters, are
automatically extracted. The extraction procedure used depends on the type
of fuzzy model to be built. In our case, fuzzy models of the type Takagi-
Sugeno are considered.
Step 4: Similarity Based Simplification
x In order to upgrade or improve the transparency and the computational
issues, the initial fuzzy model is simplified in this step. By selecting an
acceptable degree of similarity (redundancy) between the fuzzy sets in the
model, it is possible to generate models with varying degrees of complexity
for different purposes. Thereafter, depending upon the needs, an
appropriate model can be selected for validation.
Step 5: Model Evaluation
x The ultimate version of the fuzzy model built undergoes an evaluation
process that is decisive for its final acceptance for the given purpose. In
addition to the numerical model validation by simulation, the interpretation
of the fuzzy model plays an important role in the process of model
validation. This includes the analysis of the input space coverage by the
rules. If the rule base generated is found to be incomplete, i.e . if no rule is
available involving an antecedent fuzzy set, then some additional rule is to
be provided to complete the rule base. Such, an interpretation is made
easier by the simplification in step 4.
Very often, the number of rules, and hence the number of clusters, are not known a
priori . From the function approximation point of view creation, of too many