Fuzzy Logic Approach - Computational Intelligence in Time Series Forecasting - page 153

4.5 Automated Generation of Fuzzy Rule Base

From the description of the various fuzzy logic systems it is well understood that
the fuzzy inference system, i.e. the fuzzy inference engine requires a fuzzy rule
base containing a complete set of well-consistent rules that model the system to be
investigated. The automated generation of such a rule base, based on the time
series data, and later its application to time series forecasting is our prime interest.

4.5.1 The Rules Generation Algorithm

The idea of data-driven automated rule generation, presented in this section,
originates from Wang and Mendel (1992), who have proposed an adequate
procedure for it's practical implementation. In addition, we have proposed a few
modifications of those described by Wang and Mendel (1992), based on scaled and
normalized time series data, partitioned into multi-input single-output data sets.
For example, for a two-input one-output fuzzy logic system using the Wang
and Mendel's approach the input-output partitioning would be

1 1 k k

1 k

, , ; " ; , , etc .

XXY X XY

1 2 1 2

To generate the fuzzy rules automatically from these input-output partitioned data
that represent the mapping of the input values to the respective output values, each
X and Y domain will be divided into fuzzy regions and for each variable the
universe of discourse (UD) obtained by considering the values [Min ( X ), Max ( X )]
or, [Min ( Y ), Max ( Y )] of that variable. Thereafter, the UD is divided into a number
of overlapping (fuzzy) regions and to each region a membership function, usually
one of the triangular form, is assigned. This is followed by the fuzzification of
crisp input-output values, in which a mapping of crisp input/output value from the
domain into the unit interval is performed, and consequently for each membership
function the corresponding label or the membership grade is obtained. Owing to
overlapping of the fuzzy sets, more than one grade of membership may exist for
each input or output value, out of which the fuzzy set with maximum grade is
selected. The fuzzy input-output data pair, obtained for an individual input-output
data set when connected through fuzzy logic operators, define the corresponding
fuzzy rule. Here, however, conflict situations can arise when rules with the same
antecedents, i.e. the same IF parts, but with different consequents (the THEN
parts), are generated. To overcome this, to each conflicting rule a degree or a grade
is assigned, for instance,

DRule P X P X P Y ,

A 1 B 2 C

for the given

Rule: IF ( X 1 = A ) AND ( X 2 = B ), THEN ( Y = C ).