aggregateConsequents: Aggregation of fired consequents into a resulting fuzzy set

In beerda/lfl: Linguistic Fuzzy Logic

Aggregation of fired consequents into a resulting fuzzy set

Description

Take a character vector of consequent names, a numeric vector representing the degree of consequents' firing and a matrix that models fuzzy sets corresponding to the consequent names, and perform an aggregation of the consequents into a resulting fuzzy set.

Usage

aggregateConsequents(
  conseq,
  degrees,
  partition,
  firing = lukas.residuum,
  aggreg = pgoedel.tnorm
)

Arguments

conseq	A character vector of consequents. Each value in the vector must correspond to a name of some column of the partition matrix. The length of this vector must be the same as of the degrees argument.
degrees	A numeric vector of membership degrees at which the corresponding consequents (see the conseq argument) are fired.
partition	A matrix of membership degrees that describes the meaning of the consequents in vector conseq: each column of the matrix corresponds to a fuzzy set that models a single consequent (of a name given by column names of the matrix), each row corresponds to a single crisp value (which is not important for this function), hence each cell corresponds to a membership degree in which the crisp value is a member of a fuzzy set modeling the consequent. Each consequent in conseq must correspond to some column of this matrix. Such matrix may be created e.g. by using fcut() or lcut() functions.
firing	A two-argument function used to compute the resulting truth value of the consequent. Function is evaluated for each consequent in conseq, with corresponding degrees value as the first argument and corresponding truth-value of the consequent (from partition) as the second argument. In default, the Lukasiewicz residuum (lukas.residuum()) is evaluated that way.
aggreg	An aggregation function to be used to combine fuzzy sets resulting from firing the consequents with the firing function. The function should accept multiple numeric vectors of membership degrees as its arguments. In default, the Goedel t-norm (pgoedel.tnorm()) is evaluated.

Details

This function is typically used within an inference mechanism, after a set of firing rules is determined and membership degrees of their antecedents are computed, to combine the consequents of the firing rules into a resulting fuzzy set. The result of this function is then typically defuzzified (see defuzz()) to obtain a crisp result of the inference.

Function assumes a set of rules with antecedents firing at degrees given in degrees and with consequents in conseq. The meaning of the consequents is modeled with fuzzy sets whose membership degree values are captured in the partition matrix.

With default values of firing and aggreg parameters, the function computes a fuzzy set that results from a conjunction (Goedel minimum t-norm) of all provided implicative (Lukasiewicz residuum) rules.

In detail, the function first computes the fuzzy set of each fired consequent by calling part\[i\] <- firing(degrees\[i\], partition\[, conseq\[i\]\]) for each i-th consequent and the results are aggregated using the aggreg parameter: aggreg(part\[1\], part\[2\], ...). In order to aggregate consequents in a Mamdani-Assilian's fashion, set firing to pgoedel.tnorm() and aggreg to pgoedel.tconorm().

Value

A vector of membership degrees of fuzzy set elements that correspond to rows in the partition matrix. If empty vector of consequents is provided, vector of 1's is returned. The length of the resulting vector equals to the number of rows of the partition matrix.

Author(s)

Michal Burda

See Also

fire(), perceive(), defuzz(), fcut(), lcut()

Examples

    # create a partition matrix
    partition <- matrix(c(0:10/10, 10:0/10, rep(0, 5),
                          rep(0, 5), 0:10/10, 10:0/10,
                          0:12/12, 1, 12:0/12),
                        byrow=FALSE,
                        ncol=3)
    colnames(partition) <- c('a', 'b', 'c')

    # the result of aggregation is equal to:
    # pmin(1, partition[, 1] + (1 - 0.5), partition[, 2] + (1 - 0.8))
    aggregateConsequents(c('a', 'b'), c(0.5, 0.8), partition)

beerda/lfl documentation built on Feb. 15, 2023, 8:15 a.m.