Transparent Fuzzy/Neuro-fuzzy Modelling - Computational Intelligence in Time Series Forecasting - page 287

Generate initial fuzzy model

For each input variable measure
the pairwise similarity between
all fuzzy sets

Select the most similar fuzzy
sets

Update the premise of
the rule base

Yes

Check whether
Similarity >Threshold

Merge the fuzzy sets

No

Check the similarity between all
fuzzy sets and universal fuzzy set in
the same domain

Remove the fuzzy set whose similarity
with the universal fuzzy set exceeds
the threshold

Measure the similarity between all
pairs of input / feature partitions

Remove the redundant inputs from the
premise of rule base

Check the equality of the rule
premise part

Merge the rules with identical premise

Recalculate the TS rules consequent
by LSE method using the training data

Obtain the transparent final
fuzzy model

Figure 7.8. Flow chart for transparent fuzzy modelling through iterative merging

7.6.2 Similarity Relations

In this approach all similar fuzzy sets per input are merged in one operation. The
fuzzy compatibility relation

> @

of size M u is calculated for each input i
= 1, 2, ..., n . The elements of compatibility relation

Cc

i ilm

are
obtained by the Jaccard similarity index (7.3). It is to be noted that the Jaccard
similarity measure is not transitive. Thus, it follows that C i is reflexive and

CSAx , Ax

ilm l i m i