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Generate Fuzzy Inference System structure from data using subtractive clustering

fismat = genfis2(Xin,Xout,radii) fismat = genfis2(Xin,Xout,radii,xBounds) fismat = genfis2(Xin,Xout,radii,xBounds,options) fismat = genfis2(Xin,Xout,radii,xBounds,options,user_centers)

`genfis2`

generates a Sugeno-type FIS structure
using subtractive clustering and requires separate sets of input and
output data as input arguments. When there is only one output, `genfis2`

may
be used to generate an initial FIS for `anfis`

training. `genfis2`

accomplishes
this by extracting a set of rules that models the data behavior.

The rule extraction method first uses the `subclust`

function
to determine the number of rules and antecedent membership functions
and then uses linear least squares estimation to determine each rule's
consequent equations. This function returns an FIS structure that
contains a set of fuzzy rules to cover the feature space.

The arguments for `genfis2`

are as follows:

`Xin`

is a matrix in which each row contains the input values of a data point.`Xout`

is a matrix in which each row contains the output values of a data point.`radii`

is a vector that specifies a cluster center's range of influence in each of the data dimensions, assuming the data falls within a unit hyperbox.For example, if the data dimension is 3 (e.g.,

`Xin`

has two columns and`Xout`

has one column),`radii`

= [0.5 0.4 0.3] specifies that the ranges of influence in the first, second, and third data dimensions (i.e., the first column of`Xin`

, the second column of`Xin`

, and the column of`Xout`

) are 0.5, 0.4, and 0.3 times the width of the data space, respectively. If`radii`

is a scalar value, then this scalar value is applied to all data dimensions, i.e., each cluster center has a spherical neighborhood of influence with the given radius.

`xBounds`

is a 2-by-*N*optional matrix that specifies how to map the data in`Xin`

and`Xout`

into a unit hyperbox, where*N*is the data (row) dimension. The first row of`xBounds`

contains the minimum axis range values and the second row contains the maximum axis range values for scaling the data in each dimension.For example,

`xBounds`

= [-10 0 -1; 10 50 1] specifies that data values in the first data dimension are to be scaled from the range [-10 +10] into values in the range [0 1]; data values in the second data dimension are to be scaled from the range [0 50]; and data values in the third data dimension are to be scaled from the range [-1 +1]. If`xBounds`

is an empty matrix or not provided, then`xBounds`

defaults to the minimum and maximum data values found in each data dimension.`options`

is an optional vector for specifying algorithm parameters to override the default values. These parameters are explained in the help text for`subclust`

. Default values are in place when this argument is not specified.`user_centers`

is an optional matrix for specifying custom cluster centers.`user_centers`

has a size of`J`

-by-`N`

where`J`

is the number of clusters and`N`

is the total number of inputs and outputs.

The input membership function type is `'gaussmf'`

,
and the output membership function type is `'linear'`

.

The following table summarizes the default inference methods.

Inference Method | Default |
---|---|

AND | `prod` |

OR | `probor` |

Implication | `prod` |

Aggregation | `max` |

Defuzzification | `wtaver` |

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