lfl (version 2.2.0)

rbcoverage: Compute rule base coverage of data

Description

This function computes rule base coverage, i.e. a an average of maximum membership degree at which each row of data fires the rules in rule base.

Usage

rbcoverage(
  x,
  rules,
  tnorm = c("goedel", "goguen", "lukasiewicz"),
  onlyAnte = TRUE
)

Value

A numeric value of the rule base coverage of given data.

Arguments

x

Data for the rules to be evaluated on. Could be either a numeric matrix or numeric vector. If matrix is given then the rules are evaluated on rows. Each value of the vector or column of the matrix represents a predicate - it's numeric value represents the truth values (values in the interval \([0, 1]\)).

rules

Either an object of class "farules" or list of character vectors where each vector is a rule with consequent being the first element of the vector. Elements of the vectors (predicate names) must correspond to the x's names (of columns if x is a matrix).

tnorm

A character string representing a triangular norm to be used (either "goedel", "goguen", or "lukasiewicz") or an arbitrary function that takes a vector of truth values and returns a t-norm computed of them.

onlyAnte

TRUE if only antecedent-part of a rule should be evaluated. Antecedent-part of a rule are all predicates in rule vector starting from the 2nd position. (First element of a rule is the consequent - see above.)

If FALSE, then the whole rule will be evaluated (antecedent part together with consequent).

Author

Michal Burda

Details

Let \(f_{ij}\) be a truth value of \(i\)-th rule on \(j\)-th row of data x. Then \(m_j = max(f_{.j})\) is a maximum truth value that is reached for the \(j\)-th data row with the rule base. Then the rule base coverage is a mean of that truth values, i.e. \(rbcoverage = mean(m_.)\).

References

M. Burda, M. Štěpnička, Reduction of Fuzzy Rule Bases Driven by the Coverage of Training Data, in: Proc. 16th World Congress of the International Fuzzy Systems Association and 9th Conference of the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT 2015), Advances in Intelligent Systems Research, Atlantic Press, Gijon, 2015.

See Also

fire(), reduce()

Examples

    x <- matrix(1:20 / 20, nrow=2)
    colnames(x) <- letters[1:10]

    rules <- list(c('a', 'c', 'e'),
                  c('b'),
                  c('d', 'a'),
                  c('c', 'a', 'b'))
    rbcoverage(x, rules, "goguen", TRUE)  # returns 1


    rules <- list(c('d', 'a'),
                  c('c', 'a', 'b'))
    rbcoverage(x, rules, "goguen", TRUE)  # returns 0.075)