Rank aggregation problem is useful to practitioners in political
science, computer science, social science, medical science, and allied
fields. The objective is to identify a consensus ranking of n objects
that best fits independent rankings given by k different judges. Under
the Kemeny framework, a distance metric called Kemeny distance is
minimized to obtain consensus ranking. The problem is of the n! order
and quickly becomes infeasible. To address the problem, two
heuristics-based algorithms — FUR and SIgFUR — are developed in the
current package, **RankAggSIgFUR** (pronounced as
*rank-agg-cipher*). The proposed algorithms are polynomially
bounded algorithms to aggregate complete rankings under Kemeny’s
axiomatic framework. These algorithms in turn depend on newly developed
basic algorithms, *Subiterative Convergence* and *Greedy
Algorithm*. The results are generally superior to existing
algorithms in terms of both performance (Kemeny distance) and run-time.
Even for large number of objects, the proposed algorithms run in few
minutes. Please see Badal and Das
(2018). for more details.

This package is live on CRAN. The programs are in stable development phase. Each ranking could be given the corresponding weights in the version 1.0.0. This could, for example, help in reducing the size of the problem from k judges to a much fewer judges. Any major changes for complete rankings is unlikely at this time. New additions to include tied or incomplete rankings may be added over time.

Most stable version pushed to CRAN can be installed directly from CRAN:

`install.packages("RankAggSIgFUR")`

The latest version of the package under development can be installed from GitHub:

```
install.packages("devtools")
library(devtools)
remotes::install_github("prakashvs613/RankAggSIgFUR")
```

Please submit any bugs or issues (or suggestions) using the issues tab of the repo.

The main functions users will use are `fur`

and
`sigfur`

. These are heuristics-based algorithm to find
consensus rankings. The outcomes are returned as consensus ranking (in
terms of ordering), total Kemeny distance of the consensus ranking, and
extended correlation coefficient as defined by Emond and Mason (2002).

```
library(RankAggSIgFUR)
# One subiteration length
input_rkgs <- matrix(c(3, 2, 5, 4, 1, 2, 3, 1, 5, 4, 5, 1, 3, 4, 2, 1, 2, 4, 5, 3),
byrow = FALSE, ncol = 4)
subit_len_list <- 2
search_radius <- 1
fur(input_rkgs, subit_len_list, search_radius) # Determined the consensus ranking, total Kemeny
# distance, and average tau correlation coefficient
# Multiple subiteration lengths
input_rkgs <- matrix(c(3, 2, 5, 4, 1, 2, 3, 1, 5, 4, 5, 1, 3, 4, 2, 1, 2, 4, 5, 3),
byrow = FALSE, ncol = 4)
subit_len_list <- c(2,3)
search_radius <- 1
fur(input_rkgs, subit_len_list, search_radius)
# Included dataset of 15 input rankings of 50 objects
data(data50x15)
input_rkgs <- as.matrix(data50x15[, -1])
subit_len_list <- c(2, 3)
search_radius <- 1
fur(input_rkgs, subit_len_list, search_radius)
## Four input rankings of five objects
input_rkgs <- matrix(c(3, 2, 5, 4, 1, 2, 3, 1, 5, 4, 5, 1, 3, 4, 2, 1, 2, 4, 5, 3),
byrow = FALSE, ncol = 4)
subit_len_list_sbi <- c(2:3)
omega_sbi <- 10
subit_len_list_fur <- c(2:3)
search_radius <- 1
sigfur(input_rkgs, subit_len_list_sbi, omega_sbi, subit_len_list_fur, search_radius) # Determined the consensus ranking,
# total Kemeny distance, and average tau correlation coefficient
# Included dataset of 15 input rankings of 50 objects
data(data50x15)
input_rkgs <- as.matrix(data50x15[, -1])
subit_len_list_sbi <- c(3)
omega_sbi <- 5
subit_len_list_fur <- c(2:3)
search_radius <- 1
sigfur(input_rkgs, subit_len_list_sbi, omega_sbi, subit_len_list_fur, search_radius)
```

Check out the vignettes for more examples and details.

This package is released in the public domain under the General Public License GPL.

Badal PS, Das A (2018). “Efficient algorithms using subiterative
convergence for Kemeny ranking problem.” *Computers & Operations
Research*, *98*, 198-210. doi: 10.1016/j.cor.2018.06.007.

Emond EJ, Mason DW (2002). “A new rank correlation coefficient with
application to the consensus ranking problem.” *Journal of
Multi-Criteria Decision*, *11*(1), 17-28. doi: 10.1002/mcda.313.