RoughSets (version 1.0-0)

BC.IND.relation.RST: Indiscernibility relation based on rough set theory

Description

This is a function that implements a fundamental part of RST: the indiscernibility relation. The indiscernibility relation is a binary relation showing whether two objects can be discerned. The detailed description based on theoritical point of view can be seen in A.Introduction-RoughSets.

Usage

BC.IND.relation.RST(decision.table, attribute = NULL)

Arguments

decision.table

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

attribute

a numerical vector expressing indexes of subsets of attributes to be considered. The default value is NULL which means that all condition attributes will be considered. It should be noted that in this case, all attributes considered s

Value

• A class "IndiscernibilityRelation" which contains
  • IND.relation: a list representing indiscernibility relation over all objects.
  • type.relation: it is"equivalence".
  • type.model: a string showing the type of model which is used. In this case, it is"RST"which means fuzzy rough set theory.

Details

This function is used as a basic function and is needed by other functions such as BC.LU.approximation.RST, BC.positive.reg.RST for calculating lower and upper approximation and determining the positive region. The formula of the indiscernibility relation has been explained in A.Introduction-RoughSets.

References

Z. Pawlak, "Rough Sets", International Journal of Computer and Information Sciences, vol. 11, no. 5, p. 341 - 356 (1982).

See Also

BC.LU.approximation.RST, BC.LU.approximation.RST

Examples

#############################################
## Example 1: Using simple data set
## Objects must be nominal/symbolic values
## Otherwise, we must use discretization first
#############################################
## Construct decision table as data frame
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))

## In this case, we only consider the second and third attributes.
P <- c(2,3)

####### Perform indiscernibility relation #######
IND <- BC.IND.relation.RST(decision.table, attribute = P)