I am using the ComplexHeatmap package to represent the intersection among different GRanges. The vignette has some nice example to plot it:

library(circlize)
library(ComplexHeatmap)
library(GenomicRanges)
lt2 = lapply(1:4, function(i) generateRandomBed())
lt2 = lapply(lt2, function(df) GRanges(seqnames = df[, 1], 
    ranges = IRanges(df[, 2], df[, 3])))
names(lt2) = letters[1:4]
m = make_comb_mat(lt2)
UpSet(m)

It is very handy. However, the UpSet function do not plot the intersection numbers above each bar such as the sister function upset in the UpSetR package:

library('UpSetR')
movies <- read.csv( system.file("extdata", "movies.csv", package = "UpSetR"), 
                    header=T, sep=";" )

require(ggplot2); require(plyr); require(gridExtra); require(grid);

upset(movies, 
      sets = c("Action", "Comedy", "Drama"), 
      order.by="degree", matrix.color="blue", point.size=5,
      sets.bar.color=c("maroon","blue","orange"))

The upset function do not allow the m object. Thus, I suppose I need to use UpSet in my case. However, could someone help me to get the correspondent number above the bars? I could not find a parameter to easily plot it or even how the internal functions define it. I would be grateful for any help.

I am not sure whether it is a good idea to put numbers close to the bars, because you can easily get these numbers from the axis.

Since the annotations are just simple barplots annotations, you can use decorate_annotation() function to add these numbers. Currently, the solution to your problem is as follows:

library(circlize)
library(ComplexHeatmap)
library(GenomicRanges)
lt2 = lapply(1:4, function(i) generateRandomBed())
lt2 = lapply(lt2, function(df) GRanges(seqnames = df[, 1], 
    ranges = IRanges(df[, 2], df[, 3])))
names(lt2) = letters[1:4]

m = make_comb_mat(lt2)
cs = comb_size(m)
ht = UpSet(m, top_annotation = upset_top_annotation(m, ylim = c(0, 1.1*max(cs))))
ht = draw(ht)
co = column_order(ht)

nc = ncol(m)
decorate_annotation("Intersection\nsize", {
    grid.text(cs[co], 
        x = 1:nc, 
        y = unit(cs[co], "native") + unit(1, "mm"), 
        gp = gpar(fontsize = 5), 
        just = "bottom",
        default.units = "native")
})

If you check the source code of upset_top_annotation() which draws the top barplot annotation, you will find the name for this annotation is Intersection\nsize, then you can use decorate_annotation() to go back to the barplot area and add text in it.