lower {EvCombR}

Lower Bounds Based on Evidence Structure

Description

Calculate the lower bounds for a vector of sets

Usage

lower(x, sets)

Arguments

x

credal set or mass function

sets

vector of sets where each set is represented by state names separated by "/". If sets are missing, lower bounds on singletons are calculated.

Value

lower bound of mass or probability for each set in the vector sets or if sets is missing lower bounds on singletons

Note

This is equivalent to belief in Dempster-Shafer theory

Author(s)

Alexander Karlsson

References

Shafer, G., (1976), A Mathematical Theory of Evidence Princeton University Press

Walley, P. (2000), Towards a unified theory of imprecise probability, International Journal of Approximate Reasoning, 24, 125-148

See Also

upper

Examples

# state space
stateSpace <- c("a", "b", "c")

# mass function
m <- mass(list("a"=0.1, "b"=0.1 , 
               "c"=0.4, "a/b/c"=0.4), stateSpace)

# credal set
c <- credal(c(0.1, 0.1, 0.1), 
            c(0.8, 0.8, 0.8), stateSpace)

# calculate lower bounds
lower(m, c("a", "a/b"))
lower(c, c("a", "a/b"))

# lower bounds on singletons
lower(m)