RoughSets (version 1.0-0)

BC.positive.reg.RST: Regions based on rough set theory

Description

It is a function used to implement a fundamental concept of rough set theory: positive region and degree of dependency. The explanation about this concept can be seen in A.Introduction-RoughSets.

Usage

BC.positive.reg.RST(decision.table, roughset)

Arguments

decision.table

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

roughset

a "LowerUpperApproximation" class representing rough sets that are produced by BC.LU.approximation.RST.

Value

• A class "PositiveRegion" containing the following components:
  • positive.reg: a vector containing indexes of objects belonging to the positive region.
  • degree.dependency: a value of degree of dependency.
  • type.model: a string showing type of the used model. In this case, it is"RST"means rough set theory.

Details

In order to compute the function, we need to calculate the indiscernibility relation by executing BC.IND.relation.RST and the lower and upper approximations by calling BC.LU.approximation.RST.

References

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

See Also

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

and BC.positive.reg.FRST

Examples

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 consider second and third attributes only
P <- c(2,3)

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

####### Perform lower and upper approximations #####
decision.attr <- c(5)
roughset <- BC.LU.approximation.RST(decision.table, IND, decision.attr)

####### Determine the positive region ######
region <- BC.positive.reg.RST(decision.table, roughset)