RoughSets (version 1.0-0)

BC.discernibility.mat.RST: The decision-relative discernibility matrix based on rough set theory

Description

This is a function that builds the decision-relative discernibility matrix based on rough set theory.

Usage

BC.discernibility.mat.RST(decision.table,
    range.object = NULL, show.discernibilityMatrix = FALSE)

Arguments

decision.table

a "DecisionTable" class representing a decision table. See SF.asDecisionTable.

range.object

a vector representing considered objects to construct the $k$-relative discernibility matrix. The default value is NULL which means that we are using all objects in the decision table.

show.discernibilityMatrix

a boolean value determining whether the discernibility matrix will be shown or not.

Value

• A class "DiscernibilityMatrix" containing the following components:
  • disc.mat: a matrix showing the decision-relative discernibility matrix$M(\mathcal{A})$which contains$n \times n$where$n$is the number of objects.
  • disc.list: it refers to the decision-relation discernibility matrix in a list format.
  • discernibility.type: it is"RST".
  • type.model: in this case, it is"RST".

Details

It was proposed by (A. Skowron and C. Rauszer, 1992) and is used to find all reducts. A discernibility matrix of the decision table $DT = (U, C \cup D)$ is a symmetric $|U| \times |U|$ matrix with entries defined as

$c_{ij} = {a \in C|a(x_{i}) \neq a(x_{j})}, i,j = 1,...,|U|$

each $c_{ij}$ contains those attributes that differ between objects $i$ and $j$. The detailed explanation can be seen in A.Introduction-RoughSets.

References

A. Skowron and C. Rauszer, "The Discernibility Matrices and Functions in Information Systems", in: R. Slowinski (Ed.), Intelligent Decision Support: Handbook of Applications and Advances of Rough Sets Theory, Kluwer Academic Publishers, Dordrecht, Netherland, p. 331 - 362 (1992).

See Also

BC.IND.relation.RST, BC.LU.approximation.RST, and BC.LU.approximation.FRST

Examples

#######################################################################
## Example 1: Constructing the decision-relative discernibility matrix
#######################################################################
dt.ex1 <- data.frame(c(1,0,2,1,1,2,2,0), c(0, 1,0, 1,0,2,1,1),
                        c(2,1,0,0,2,0,1,1), c(2,1,1,2,0,1,1,0), c(0,2,1,2,1,1,2,1))
colnames(dt.ex1) <- c("aa", "bb", "cc", "dd", "ee")
decision.table <- SF.asDecisionTable(dataset = dt.ex1, decision.attr = 5,
                                     indx.nominal = c(1:5))

## build the decision-relation discernibility matrix
res.1 <- BC.discernibility.mat.RST(decision.table, range.object = NULL)