WM: WM model building

Description

This is the internal function that implements the model proposed by L. X. Wang and J. M. Mendel. It is used to solve regression task. Users do not need to call it directly, but just use frbs.learn and predict

Usage

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WM(data.train, num.labels, type.mf = "GAUSSIAN", type.tnorm = "PRODUCT",
  type.implication.func = "ZADEH", classification = FALSE,
  range.data = NULL)

Arguments

data.train

a matrix (m \times n) of normalized data for the training process, where m is the number of instances and n is the number of variables; the last column is the output variable. Note the data must be normalized between 0 and 1.

num.labels

a matrix (1 \times n), whose elements represent the number of labels (linguistic terms); n is the number of variables.

type.mf

the type of the membership function. See frbs.learn.

type.tnorm

a value which represents the type of t-norm. See inference.

type.implication.func

a value representing type of implication function. Let us consider a rule, a \to b,

  • DIENES_RESHER means (b > 1 - a? b : 1 - a).

  • LUKASIEWICZ means (b < a ? 1 - a + b : 1).

  • ZADEH means (a < 0.5 || 1 - a > b ? 1 - a : (a < b ? a : b)).

  • GOGUEN means (a < b ? 1 : b / a).

  • GODEL means (a <= b ? 1 : b).

  • SHARP means (a <= b ? 1 : 0).

  • MIZUMOTO means (1 - a + a * b).

  • DUBOIS_PRADE means (b == 0 ? 1 - a : (a == 1 ? b : 1)).

  • MIN means (a < b ? a : b).

classification

a boolean representing whether it is a classification problem or not.

range.data

a matrix representing interval of data.

Details

The fuzzy rule-based system for learning from L. X. Wang and J. M. Mendel's paper is implemented in this function. For the learning process, there are four stages as follows:

The outcome is a Mamdani model. In the prediction phase, there are four steps: fuzzification, checking the rules, inference, and defuzzification.

References

L.X. Wang and J.M. Mendel, "Generating fuzzy rule by learning from examples", IEEE Trans. Syst., Man, and Cybern., vol. 22, no. 6, pp. 1414 - 1427 (1992).

See Also

frbs.learn, predict and frbs.eng.


Questions? Problems? Suggestions? or email at ian@mutexlabs.com.

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