This function displays several components of the object.
The components of one particular method can be different
from components of other methods. The following is a
description of all components which might be printed.
The name of the model: A name given by
the user representing the name of the simulation or data
or model.
Model was trained using: It shows which
method we have been used.
The interval of training
data: It is a matrix representing the original interval
of data where the first and second rows are minimum and
maximum of data, respectively. The number of columns
represents the number of variables.
The number of
fuzzy terms of the input variables: Given as elements of
a matrix.
The names of fuzzy terms of the input
variables: These names are generated automatically by
frbs expressing all fuzzy terms considered. These names
are built by two parts which are the name of variables
expressed by "v" and the name of fuzzy labels of each
variables represented by "a". For example, "v.1-a.1"
means the fuzzy label "a.1" of the first variable (v.1).
The names of fuzzy terms of the output variable:
For the Mamdani model, since the frbs package only
considers single output, the names of the fuzzy terms for
the output variable are simple and clear and start with
"c". However, for Takagi Sugeno Kang model and fuzzy
rule-based classification systems, this component is
always NULL.
The parameter values of membership
functions of the input variables (normalized): It is
represented by a matrix (5 x n) where n depends on the
number of fuzzy terms on the input variables and the
first row of the matrix describes a type of membership
function, and the rest of rows are their parameter
values. For example, label "v.1-a.2" has value {4.0,
0.23, 0.43, 0.53, 0.73} on its column. It means that the
label a.2 of variable v.1 has a parameter as follows.
4.0 on the first row shows trapezoid shape in the middle
position, while 0.23, 0.43, 0.53, and 0.73 are corner
points of a trapezoid. Furthermore, the following is the
complete list of shapes of membership functions:
Triangular: 1 on the first row and rows
2, 3, and 4 represent corner points.
Trapezoid: 2,
3, or 4 on the first row means they are trapezoid in
left, right and middle side, respectively, and rows 2, 3,
4, and 5 represent corner points. But for trapezoid at
left or right side the fifth row is NA.
Gaussian:
5 on the first row means it uses Gaussian and second and
third row represent mean and variance.
Sigmoid: 6
on the first row and two parameters (gamma and c) on
second and third rows.
Generalized bell: 7 on the
first row and three parameters (a, b, c) on second,
third, and fourth rows.
The fuzzy IF-THEN rules:
In this package, there are several models for
representing fuzzy IF-THEN rules based on the method
used.
Mamdani model: they are
represented as a knowledge base containing two parts:
antecedent and consequent parts which are separated by a
sign "->", as for example in the following rule:var.1 is v.1-a.1 and var.2 is v.2-a.2 -> var.3 is
c.2
Takagi Sugeno Kang model: In this model, this
component only represents the antecedent of rules while
the consequent part will be represented by linear
equations.
fuzzy rule-based classification
systems: This model is quite similar to the Mamdani
model, but the consequent part expresses pre-defined
classes instead of linguistic values.
approximate
approach: Especially for GFS.FR.MOGUL, a matrix of
parameters of membership functions is used to represent
the fuzzy IF-THEN rules as well. The representation of
rules and membership functions is a matrix (n x (p x m))
where n is the number of rules and m is the number of
variables while p is the number of corner points of the
membership function, if we are using triangular or
trapezoid then p = 3 or 4, respectively. For example,
let us consider the triangular membership function and a
number of variables of 3. The representation of rules
and membership functions is as follows: <>
<> <>.
The linear equations on consequent parts of fuzzy
IF-THEN rules: It is used in the Takagi Sugeno Kang
model.
The weight of the rules or the certainty
factor: For the FRBCS.W method, this shows the weight
related to the rules representing the ratio of dominance
among the rules.
The cluster centers: This
component is used in clustering methods representing
cluster centers.