A First Course in FUZZY and NEURAL CONTROL

270 CHAPTER 8. APPLICATIONS

R^9 :Ifareais large andsolidityis medium andEdifis small, then trash type

is bark.

R^10 :Ifareais large andsolidityis medium andEdifis large, then trash type

is stick.

R^11 :Ifareais large andsolidityis large andEdifis small, then trash type is

leaf.

R^12 :Ifareais large andsolidityis large andEdifis large, then trash type is

stick.

Generally, the number of rules for any system is the product of the number of
linguistic values of all the linguistic variables. Since we have two linguistic values
{small, large} forareaandEdif and three linguistic values {small, medium,
large} forsolidity,we have a total of 12 fuzzy rules. The 12 rules that describe
the trash types are summarized in Table 8.6.

Table 8.6. TSK fuzzy rules for trash

identification with 232-partition^1

IF AND AND THEN

Rule Areais Solidityis Edifis Trash Type is

R^1 Small Small Small Pepper

R^2 Small Small Large Pepper

R^3 Small Medium Small Pepper

R^4 Small Medium Large Pepper

R^5 Small Large Small Pepper

R^6 Small Large Large Pepper

R^7 Large Small Small Bark

R^8 Large Small Large Bark

R^9 Large Medium Small Bark

R^10 Large Medium Large Stick

R^11 Large Large Small Leaf

R^12 Large Large Large Stick

Based on these rules, the ANFIS is trained to modify the premise parameters
and the consequent parameters for a given pair of input-output training pairs.
The outputs at Layer 4 of the ANFIS structure are

fi=ai 0 +ai 1 x 1 +ai 2 x 2 +ai 3 x 3 i=1,∑∑∑, 12

(^1) The membership partition of the input variablearea,solidity,andEdifare {(Small,
Large), (Small, Medium, Large), (Small, Large)} and is represented as 232-partition in the
text.