The summary function for frbs objects

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Description

This function enables the output of a summary of the frbs-object.

Usage

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## S3 method for class 'frbs'
summary(object, ...)

Arguments

object

the frbs-object

...

the other parameters (not used)

Details

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 names of attributes: a list of names of training data.

  • 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.

  • Type of FRBS model: a description expresses one of the following FRBS model available such as "MAMDANI", "TSK", "FRBCS", "CLUSTERING", "APPROXIMATE", and "2TUPPLE".

  • Type of membership function: a description expresses one of the following shapes of membership functions: "GAUSSIAN", code"TRIANGLE", "TRAPEZOID", "SIGMOID", and "BELL".

  • Type of t-norm method: a description expresses one of the following type of t-norm: "MIN", "PRODUCT", "HAMACHER", "YAGER", and "BOUNDED".

  • Type of s-norm method: a description expresses one of the following type of s-norm: "MAX", "SUM", "HAMACHER", "YAGER", and "BOUNDED".

  • Type of defuzzification technique: a description expresses one of the following types: "WAM", "FIRST_MAX", "LAST_MAX", "MEAN_MAX", and "COG".

  • Type of implication function: a description expresses one of the following types: "DIENES_RESHER", "LUKASIEWICZ", "ZADEH", "GOGUEN", "GODEL", "SHARP", "MIZUMOTO", "DUBOIS_PRADE", and "MIN".

  • The names of linguistic terms of the input variables: These names are generated automatically by frbs expressing all linguistic terms considered. Generally, these names are built by two parts which are the name of variables expressed by "v" and the name of linguistic terms of each variables represented by "a". For example, "v.1_a.1" means the linguistic value "a.1" of the first variable (v.1). However, we provide different format if we set the number of linguistic terms (num.labels) to 3, 5, 7. For example, for the number of label 3, it will be "small", "medium", and "large".

  • The names of linguistic terms of the output variable: For the Mamdani model, since the frbs package only considers single output, the names of the linguistic terms for the output variable are simple and clear and start with "c". However, for the 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 \times n) where n depends on the number of linguistic 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:

    • TRIANGLE: 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.

    • 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.

    • the Mamdani model: they are represented as a knowledge base containing two parts: antecedent and consequent parts which are separated by a sign "THEN", as for example in the following rule:

      IF var.1 is v.1_a.1 and var.2 is v.2_a.2 THEN var.3 is c.2

    • the 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 (FRBCS): This model is quite similar to the Takagi Sugeno Kang model, but the consequent part expresses pre-defined classes instead of a simplify of linear equations.

    • 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 \times (p \times 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 TRIANGLE 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:

      <<a11 a12 a13>> <<b11 b12 b13>> <<c11 c12 c13>>.

  • 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.

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