Soft Computing and Its Applications, Volume One

Fuzzy Implications and Fuzzy If-Then Models 455

FIGURE 43 Merging two neighboring rules with different consequents.

Denition 4.12 Rule base

R



obtained from R by merging rules with different

antecedents and consequents, applying CNF union in both the antecedent and conse-

quent parts is called a cover of R.

A connection of compression and cover is the following:

Remark 4.7 The minimal cover

↔

R



of the minimal compression

R



of rule base R

is identical with the minimal cover

↔

R

of R. Here “minimal” means that all possible

rules are united.

The proof is rather straightforward from the denitions. From the two types of

rule merging by the CNF union, ...