Advances in Fuzzy Systems

Research Article

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

Algorithm 1

 FLR training algorithm.
S0. The first input ( π‘Ž 0 , 𝐢 0 ) is memorized. A t an instant, there are 𝑐 Known
Classes 𝐢 1 , … , 𝐢 𝑐 memorized in the memory, initially 𝑐 = 0 .
S1.   Present the next input ( π‘Ž 𝑖 , 𝐢 π‘˜ ) , 𝑖 = 1 , . . . , π‘š to the initially β€œset” family of rules.
S2.  If no rules are β€œset” then
Store input ( π‘Ž 𝑖 , 𝐢 𝐾 ) ,
𝑐 = 𝑐 + 1 ,
     Go to S1.
   Else
Compute π‘˜ ( π‘Ž 0 , π‘Ž 𝑖 ) , 𝑖 = 1 , … , 𝑐 of the β€œset” rules.
S3.    Competition among the β€œset” rules:
     Winner is rule ( π‘Ž 𝐽 , 𝐢 𝐽 ) such that 𝐽 = a r g m a x { π‘˜ ( π‘Ž 0 , π‘Ž 𝑖 ) } , 𝑖 = 1 , … , 𝑐 .
S4.    The Assimilation Condition:
   Both 𝑍 ( π‘Ž 𝑖 ∨ π‘Ž 𝐽 ) ≀ 𝜌 and 𝐢 𝑖 = 𝐢 𝐽 .
S5.     If the Assimilation Condition is satisfied then
   Replace π‘Ž 𝐽 by π‘Ž 0 ∨ π‘Ž 𝐽 .
      Else
    β€œreset” the winner ( π‘Ž 𝐽 , 𝐢 𝐽 ) , Go to S2.