Fuzzy Logic Approach - Computational Intelligence in Time Series Forecasting - page 157

D ( Rule 2) = P S1 ( X 21 ). P S1 ( X 22 ). P CE ( X 23 ). P B1 ( X 24 ). P B2 ( Y 2 )

= (0.6).(0.8).(0.8).(0.6).(0.8) = 0.18432
respectively, and both are found to be same in this example. However, they are
usually different for realistic time series data.

Step 4: building of combined fuzzy rule base

A combined fuzzy rule base, built in the following way, is shown in Figure 4.3(c).
It is a lookup table to be explained on the example of a two inputs [ X k 1 , X k 2 ], one
output Y 1 system for simplicity. Individual boxes are filled with fuzzy rules
generated from input-output data, whereby the AND-rules fill only one box and the
OR-rules fill all the boxes in the rows and/or columns corresponding to the regions
of their IF parts. If there is more than one rule in one box, then the rule with the
maximum degree is taken. For example, the rule
Rule: IF X k1 is B1 OR X k2 is B2 THEN Y 1 is S2
fills five boxes in the column of B1 and five boxes in the row of B2 with S2. The
degrees of all the S2's in these boxes are equal to the degree of the OR-rule,
whereas the same rule with AND, instead of OR, fills only the intersection of
column B1 and row B2 with S2

X k 1

S1 S2 CE B1 B2

S1 S1 S2

S2 B1 S2

X k 2

S1 S2

CE

B1 CE S2

S2 S2 S2 S2 S2

B2

Figure 4.3(c). Look-up table for fuzzy rule base

The combined rule base of Figure 4.3(c) describes the following fuzzy rules:

IF X k1 is S2 AND X k2 is S1 THEN Y 1 is S1
IF X k1 is CE AND X k2 is S2 THEN Y 1 is B1
IF X k1 is S1 AND X k2 is B1 THEN Y 1 is CE
IF X k1 is S2 AND X k2 is CE THEN Y 1 is S1
IF X k1 is B1 OR X k2 is B2 THEN Y 1 is S2

It is to be noted that for a system with more than two inputs the above table would
require a multidimensional space for its presentation.