Research Article

# Fuzzy Lattice Reasoning for Pattern Classification Using a New Positive Valuation Function

## Algorithm 1

βFLR training algorithm.
 S0. The first input ( π 0 , πΆ 0 ) is memorized. A t an instant, there are π Known Classes πΆ 1 , β¦ , πΆ π memorized in the memory, initially π = 0 . S1. β Present the next input ( π π , πΆ π ) , π = 1 , . . . , π to the initially βsetβ family of rules. S2. βIf no rules are βsetβ then Store input ( π π , πΆ πΎ ) , π = π + 1 , βββββGo to S1. βββElse Compute π ( π 0 , π π ) , π = 1 , β¦ , π of the βsetβ rules. S3. βββCompetition among the βsetβ rules: βββββWinner is rule ( π π½ , πΆ π½ ) such that π½ = a r g m a x { π ( π 0 , π π ) } , π = 1 , β¦ , π . S4. βββThe Assimilation Condition: βββBoth π ( π π β¨ π π½ ) β€ π and πΆ π = πΆ π½ . S5. ββββIf the Assimilation Condition is satisfied then βββReplace π π½ by π 0 β¨ π π½ . β ββββElse βββ βresetβ the winner ( π π½ , πΆ π½ ) , Go to S2.

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