# Combining Basic Probability Assignments These functions can be used to combine one or several basic probability assignments (bpa). In the limited context that we support here, a bpa is nothing but a discrete distribution, that may have an additional mass for ignorance. The suffix tells how the combination will be done : `ds` denotes that the Dempster-Shafer rules will be used, `bs` denotes that Bayes' rule will be used. Thus the function `combine.ds` combines two numeric vectors by Dempster-Shafer rules. The first middle denotes what kind of object a function operates on. Thus `combine.bpa.ds` combines two `bpa` objects by Dempster-Shafer rules, while `combine.bpamat.ds` does the same for two bpamat objects. Finally, the second middle may be used - if set to `list`, it combines lists of objects. Thus, the function `combine.bpa.list.ds` combines lists of `bpa` objects by Dempster-Shafer rules. ```r combine.bs(x, y) combine.ds(x, y) combine.bpa.bs(b1, b2) combine.bpa.ds(b1, b2) combine.bpa.list.bs(blist) combine.bpa.list.ds(blist) combine.bpamat.bs(bmat1, bmat2) combine.bpamat.ds(bmat1, bmat2) combine.bpamat.list.bs(bmatlist) combine.bpamat.list.ds(bmatlist) ``` ## Arguments - `x`: A numeric vector representing a bpa. - `y`: A numeric vector representing a bpa. - `b1`: The first bpa object that needs to be combined. - `b2`: The second bpa object that needs to be combined. - `blist`: A list of bpa's to be be combined. - `bmat1`: The first bpa matrix that needs to be combined. - `bmat2`: The second bpa matrix that needs to be combined. - `bmatlist`: A list of bpa matrices to be be combined. ## Returns The `combine.ds` functions returns a numeric vector representing the new bpa. The `combine.bpamat.bs`, `combine.bpamat.ds`, `combine.bpamat.list.bs` and `combine.bpamat.list.bs` functions themselves returns a bpamat object. The `combine.bpa.bs`, `combine.bpa.ds`, `combine.bpa.list.bs` and the `combine.bpa.list.ds` functions themselves returns a bpa object. ## References Gordon, J. and Shortliffe, E. H. (1984). The dempster-shafer theory of evidence. Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project, 3:832-838. Shafer, G. (1986). The combination of evidence. International Journal of Intelligent Systems, 1(3):155-179. ## Author(s) Mohit Dayal ## Examples ```r ##Very Strong, Consistent Testimony vstrong <- c(0.85, 0.07, 0.08) ##Strong, Consistent Testimony strong <- c(0.7, 0.15, 0.15) ##Somewhat Ambiguous Testimony amb <- c(0.55, 0.40, 0.05) ##More Diffuse Testimony amb2 <- c(0.55, 0.20, 0.25) fn_gen <- function(par) { x <- gtools::rdirichlet(2, par) y <- x y <- t(apply(y, MARGIN = 1, FUN = function(x) x * 0.9)) y <- cbind(y, 0.1) return(y) } a1 <- fn_gen(vstrong) combine.bs(a1[1,], a1[2,]) combine.ds(a1[1,], a1[2,]) a2 <- fn_gen(strong) combine.bs(a2[1,], a2[2,]) combine.ds(a2[1,], a2[2,]) a3 <- fn_gen(amb) combine.bs(a3[1,], a3[2,]) combine.ds(a3[1,], a3[2,]) a4 <- fn_gen(amb2) combine.bs(a4[1,], a4[2,]) combine.ds(a4[1,], a4[2,]) ##For bpa or bpamat examples, see the relevant help files ```

combine function