rbcoverage: Compute rule base coverage of data In lfl: Linguistic Fuzzy Logic

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

 1 2 3 4 5 6 rbcoverage( x, rules, tnorm = c("goedel", "goguen", "lukasiewicz"), onlyAnte = TRUE )

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).

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_.).

Value

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

Michal Burda

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.