8.4. IDENTIFICATION OF TRASH IN COTTON 269
the sigmoidal membership functions are smooth and nonlinear functions and
are increasingly popular for specifying fuzzy sets. The generalized bell function
has one more parameter than the Gaussian membership functions, resulting in
an extra degree of freedom to adjust the steepness at the crossover points [36].
This is one of the reasons the generalized bell function is used in the formulation
of the membership functions in this example.
Fuzzy partition of input space Sinceareameasures for pepper objects are
small compared to the other types of trash, it is assigned the linguistic values
smallandlarge.Soliditymeasures for bark objects are typically small compared
to the measures for leaf and stick objects. However, for some bark objects,
this value can be slightly higher than the typical values for ideal bark objects.
Hence, the linguistic variablesolidityis assigned the valuessmall,medium,and
large.SinceEdifmeasure for bark and stick objects are the highest, while the
measures for leaf and pepper objects are small, it is assigned the values ofsmall
andlarge to distinguish the stick objects from the other trash types. Table
8.5 is a summary of the linguistic variables and the linguistic values used to
obtain the premise and consequent parameters of the ANFIS structure. Figure
8.14 illustrates the ANFIS structure developed for the identification of the trash
types [63, 64, 65, 66].
Fuzzy rules for trash identification The linguistic variablesarea,solidity,
andEdifwith the linguistic values assigned in Table 8.5 are used to develop the
Sugeno fuzzy rules for the various trash types. The fuzzy rules for describing
the four trash types are as follows:
R^1 :Ifareais small andsolidityis small andEdifis small, then trash type is
pepper.R^2 :Ifareais small andsolidityis small andEdifis large, then trash type is
pepper.R^3 :Ifareais small andsolidityis medium andEdifis small, then trash type
is pepper.R^4 :Ifareais small andsolidityis medium andEdifis large, then trash type
is pepper.R^5 :Ifareais small andsolidityis large andEdifis small, then trash type is
pepper.R^6 :Ifareais small andsolidityis large andEdifis large, then trash type is
pepper.R^7 :Ifareais large andsolidityis small andEdifis small, then trash type is
bark.R^8 :Ifareais large andsolidityis small andEdifis large, then trash type is
bark.