How can I match fuzzy match strings from two datasets?

The solution depends on the desired cardinality of your matching a to b. If it's one-to-one, you will get the three closest matches above. If it's many-to-one, you will get six.

One-to-one case (requires assignment algorithm):

When I've had to do this before I treat it as an assignment problem with a distance matrix and an assignment heuristic (greedy assignment used below). If you want an "optimal" solution you'd be better off with optim.

Not familiar with AGREP but here's example using stringdist for your distance matrix.

library(stringdist)
d <- expand.grid(a$name,b$name) # Distance matrix in long form
names(d) <- c("a_name","b_name")
d$dist <- stringdist(d$a_name,d$b_name, method="jw") # String edit distance (use your favorite function here)

# Greedy assignment heuristic (Your favorite heuristic here)
greedyAssign <- function(a,b,d){
  x <- numeric(length(a)) # assgn variable: 0 for unassigned but assignable, 
  # 1 for already assigned, -1 for unassigned and unassignable
  while(any(x==0)){
    min_d <- min(d[x==0]) # identify closest pair, arbitrarily selecting 1st if multiple pairs
    a_sel <- a[d==min_d & x==0][1] 
    b_sel <- b[d==min_d & a == a_sel & x==0][1] 
    x[a==a_sel & b == b_sel] <- 1
    x[x==0 & (a==a_sel|b==b_sel)] <- -1
  }
  cbind(a=a[x==1],b=b[x==1],d=d[x==1])
}
data.frame(greedyAssign(as.character(d$a_name),as.character(d$b_name),d$dist))

Produces the assignment:

       a          b       d
1 Ace Co    Ace Co. 0.04762
2  Bayes Bayes Inc. 0.16667
3    asd       asdf 0.08333

I'm sure there's a much more elegant way to do the greedy assignment heuristic, but the above works for me.

Many-to-one case (not an assignment problem):

do.call(rbind, unname(by(d, d$a_name, function(x) x[x$dist == min(x$dist),])))

Produces the result:

   a_name     b_name    dist
1  Ace Co    Ace Co. 0.04762
11   Baes Bayes Inc. 0.20000
8   Bayes Bayes Inc. 0.16667
12   Bays Bayes Inc. 0.20000
10    Bcy Bayes Inc. 0.37778
15    asd       asdf 0.08333

Edit: use method="jw" to produce desired results. See help("stringdist-package")

Here is a solution using the fuzzyjoin package. It uses dplyr-like syntax and stringdist as one of the possible types of fuzzy matching.

As suggested by @C8H10N4O2, the stringdist method="jw" creates the best matches for your example.

As suggested by @dgrtwo, the developer of fuzzyjoin, I used a large max_dist and then used dplyr::group_by and dplyr::slice_min to get only the best match with minimum distance. (slice_min replaces the older top_n and if the original order is important and not alphabetical, use mutate(rank = row_number(dist)) %>% filter(rank == 1))

a <- data.frame(name = c('Ace Co', 'Bayes', 'asd', 'Bcy', 'Baes', 'Bays'),
                price = c(10, 13, 2, 1, 15, 1))
b <- data.frame(name = c('Ace Co.', 'Bayes Inc.', 'asdf'),
                qty = c(9, 99, 10))

library(fuzzyjoin); library(dplyr);

stringdist_join(a, b, 
                by = "name",
                mode = "left",
                ignore_case = FALSE, 
                method = "jw", 
                max_dist = 99, 
                distance_col = "dist") %>%
  group_by(name.x) %>%
  slice_min(order_by = dist, n = 1)

#> # A tibble: 6 x 5
#> # Groups:   name.x [6]
#>   name.x price     name.y   qty       dist
#>   <fctr> <dbl>     <fctr> <dbl>      <dbl>
#> 1 Ace Co    10    Ace Co.     9 0.04761905
#> 2  Bayes    13 Bayes Inc.    99 0.16666667
#> 3    asd     2       asdf    10 0.08333333
#> 4    Bcy     1 Bayes Inc.    99 0.37777778
#> 5   Baes    15 Bayes Inc.    99 0.20000000
#> 6   Bays     1 Bayes Inc.    99 0.20000000

I am not sure if this is a useful direction for you, John Andrews, but it gives you another tool (from the RecordLinkage package) and might help.

install.packages("ipred")
install.packages("evd")
install.packages("RSQLite")
install.packages("ff")
install.packages("ffbase")
install.packages("ada")
install.packages("~/RecordLinkage_0.4-1.tar.gz", repos = NULL, type = "source")

require(RecordLinkage) # it is not on CRAN so you must load source from Github, and there are 7 dependent packages, as per above

compareJW <- function(string, vec, cutoff) {
  require(RecordLinkage)
  jarowinkler(string, vec) > cutoff
}

a<-data.frame(name=c('Ace Co','Bayes', 'asd', 'Bcy', 'Baes', 'Bays'),price=c(10,13,2,1,15,1))
b<-data.frame(name=c('Ace Co.','Bayes Inc.','asdf'),qty=c(9,99,10))
a$name <- as.character(a$name)
b$name <- as.character(b$name)

test <- compareJW(string = a$name, vec = b$name, cutoff = 0.8)  # pick your level of cutoff, of course
data.frame(name = a$name, price = a$price, test = test)

> data.frame(name = a$name, price = a$price, test = test)
    name price  test
1 Ace Co    10  TRUE
2  Bayes    13  TRUE
3    asd     2  TRUE
4    Bcy     1 FALSE
5   Baes    15  TRUE
6   Bays     1 FALSE