| Title: | Weighted Ordered Weighted Average |
|---|---|
| Description: | Introduce weights into Ordered Weighted Averages and extend bivariate means based on n-ary tree construction. Please refer to the following: G. Beliakov, H. Bustince, and T. Calvo (2016, ISBN: 978-3-319-24753-3), G. Beliakov(2018) <doi:10.1002/int.21913>, G. Beliakov, J.J. Dujmovic (2016) <doi:10.1016/j.ins.2015.10.040>, J.J. Dujmovic and G. Beliakov (2017) <doi:10.1002/int.21828>. |
| Authors: | Gleb Beliakov [aut, cre], Daniela Calderon [aut] |
| Maintainer: | Gleb Beliakov <[email protected]> |
| License: | LGPL-3 |
| Version: | 1.0.2 |
| Built: | 2024-12-23 06:19:54 UTC |
| Source: | CRAN |
Various weighted multivariate extensions of bivariate and OWA functions, including implicit, quantifier-based and binary tree based WOWA.
wowa()wowa()
Lists the functions implemented in this package.
output |
No return value, called for printing only. |
Gleb Beliakov, Daniela L. Calderon, Deakin University
[1]G. Beliakov, H. Bustince, and T. Calvo. A Practical Guide to Averaging Functions. Springer, Berlin, Heidelberg, 2016.
[2]G. Beliakov. A method of introducing weights into OWA operators and other symmetric functions. In V. Kreinovich, editor, Uncertainty Modeling. Dedicated to B. Kovalerchuk, pages 37-52. Springer, Cham, 2017.
[3]G. Beliakov. Comparing apples and oranges: The weighted OWA function, Int.J. Intelligent Systems, 33, 1089-1108, 2018.
[4]V. Torra. The weighted OWA operator. Int. J. Intelligent Systems, 12:153-166, 1997.
[5]G. Beliakov and J.J. Dujmovic , Extension of bivariate means to weighted means of several arguments by using binary trees, Information sciences, 331, 137-147, 2016.
[6] J.J. Dujmovic and G. Beliakov. Idempotent weighted aggregation based on binary aggregation trees. Int. J. Intelligent Systems 32, 31-50, 2017.
wowa()wowa()
Function for Calculating implicit Weighted OWA function
wowa.ImplicitWOWA(x, p, w, n)wowa.ImplicitWOWA(x, p, w, n)
x |
The vector of inputs |
p |
The weights of inputs x |
w |
The OWA weightings vector |
n |
Dimension of the vector x |
output |
The value of the Impicit Weighted OWA |
Gleb Beliakov, Daniela L. Calderon, Deakin University
[1]G. Beliakov, H. Bustince, and T. Calvo. A Practical Guide to Averaging Functions. Springer, Berlin, Heidelberg, 2016.
[2]G. Beliakov. A method of introducing weights into OWA operators and other symmetric functions. In V. Kreinovich, editor, Uncertainty Modeling. Dedicated to B. Kovalerchuk, pages 37-52. Springer, Cham, 2017.
[3]G. Beliakov. Comparing apples and oranges: The weighted OWA function, Int.J. Intelligent Systems, 33, 1089-1108, 2018.
[4]V. Torra. The weighted OWA operator. Int. J. Intelligent Systems, 12:153-166, 1997.
[5]G. Beliakov and J.J. Dujmovic , Extension of bivariate means to weighted means of several arguments by using binary trees, Information sciences, 331, 137-147, 2016.
[6] J.J. Dujmovic and G. Beliakov. Idempotent weighted aggregation based on binary aggregation trees. Int. J. Intelligent Systems 32, 31-50, 2017.
n <- 4 example <- wowa.ImplicitWOWA(c(0.3,0.4,0.8,0.2), c(0.3,0.25,0.3,0.15), c(0.4,0.35,0.2,0.05), n) examplen <- 4 example <- wowa.ImplicitWOWA(c(0.3,0.4,0.8,0.2), c(0.3,0.25,0.3,0.15), c(0.4,0.35,0.2,0.05), n) example
Function for computing the ordered weigted averages
wowa.OWA(n, x, w)wowa.OWA(n, x, w)
n |
Dimension of the vector x |
x |
The vector of inputs |
w |
The OWA weights |
output |
The value of the ordered weighted average. |
Gleb Beliakov, Daniela L. Calderon, Deakin University
[1]G. Beliakov, H. Bustince, and T. Calvo. A Practical Guide to Averaging Functions. Springer, Berlin, Heidelberg, 2016.
n <- 4 wowa.OWA(n, c(0.3,0.4,0.8,0.2), c(0.4,0.35,0.2,0.05))n <- 4 wowa.OWA(n, c(0.3,0.4,0.8,0.2), c(0.4,0.35,0.2,0.05))
Function for calculating the Weighted Arithmetic Mean
wowa.WAM(n, x, w)wowa.WAM(n, x, w)
n |
Dimension of the array x |
x |
The vector of inputs |
w |
The vector of weights |
output |
The value of the WAM function |
Gleb Beliakov, Daniela L. Calderon, Deakin University
[1]G. Beliakov, H. Bustince, and T. Calvo. A Practical Guide to Averaging Functions. Springer, Berlin, Heidelberg, 2016.
n <- 4 wowa.WAM(n, c(0.3,0.4,0.8,0.2), c(0.3,0.25,0.3,0.15) )n <- 4 wowa.WAM(n, c(0.3,0.4,0.8,0.2), c(0.3,0.25,0.3,0.15) )
Function for calculating a binary tree multivariate extension of a binary averaging function
wowa.WAn(x, w, n, Fn, L)wowa.WAn(x, w, n, Fn, L)
x |
Vector of inputs |
w |
The weightings vector |
n |
Dimension of the array x (and w) |
Fn |
Bivariate symmetric mean that is extended to n arguments |
L |
The number of levels of the binary tree (see docs) |
output |
The output is Weighted n-variate mean extending Fn |
Gleb Beliakov, Daniela L. Calderon, Deakin University
[1]G. Beliakov, H. Bustince, and T. Calvo. A Practical Guide to Averaging Functions. Springer, Berlin, Heidelberg, 2016.
[2]G. Beliakov. A method of introducing weights into OWA operators and other symmetric functions. In V. Kreinovich, editor, Uncertainty Modeling. Dedicated to B. Kovalerchuk, pages 37-52. Springer, Cham, 2017.
[3]G. Beliakov. Comparing apples and oranges: The weighted OWA function, Int.J. Intelligent Systems, 33, 1089-1108, 2018.
[4]V. Torra. The weighted OWA operator. Int. J. Intelligent Systems, 12:153-166, 1997.
[5]G. Beliakov and J.J. Dujmovic , Extension of bivariate means to weighted means of several arguments by using binary trees, Information sciences, 331, 137-147, 2016.
[6] J.J. Dujmovic and G. Beliakov. Idempotent weighted aggregation based on binary aggregation trees. Int. J. Intelligent Systems 32, 31-50, 2017.
Fn <- function( x, y) { # just a simple arithmetic mean, # but can be more complex functions (eg heronian, Logaritmic means) out <- (x+y)/2 return(out) } n <- 4 example <- wowa.WAn(c(0.3,0.4,0.8,0.2), c(0.4,0.3,0.2,0.1), n, Fn, 10) exampleFn <- function( x, y) { # just a simple arithmetic mean, # but can be more complex functions (eg heronian, Logaritmic means) out <- (x+y)/2 return(out) } n <- 4 example <- wowa.WAn(c(0.3,0.4,0.8,0.2), c(0.4,0.3,0.2,0.1), n, Fn, 10) example
Function for extending order weigted averages and other multivariate symmetric functions
wowa.weightedf(x, p, w, n, Fn, L)wowa.weightedf(x, p, w, n, Fn, L)
x |
The vector of inputs |
p |
The weights of inputs x |
w |
The OWA weightings vector |
n |
The dimension of the vector x |
Fn |
Base n-variate symmetric function defined in R |
L |
The number of levels of the n-ary tree (see docs) |
output |
The output is the weighted ordered weigted average. |
Gleb Beliakov, Daniela L. Calderon, Deakin University
[1]G. Beliakov, H. Bustince, and T. Calvo. A Practical Guide to Averaging Functions. Springer, Berlin, Heidelberg, 2016.
[2]G. Beliakov. A method of introducing weights into OWA operators and other symmetric functions. In V. Kreinovich, editor, Uncertainty Modeling. Dedicated to B. Kovalerchuk, pages 37-52. Springer, Cham, 2017.
[3]G. Beliakov. Comparing apples and oranges: The weighted OWA function, Int.J. Intelligent Systems, 33, 1089-1108, 2018.
[4]V. Torra. The weighted OWA operator. Int. J. Intelligent Systems, 12:153-166, 1997.
[5]G. Beliakov and J.J. Dujmovic , Extension of bivariate means to weighted means of several arguments by using binary trees, Information sciences, 331, 137-147, 2016.
[6] J.J. Dujmovic and G. Beliakov. Idempotent weighted aggregation based on binary aggregation trees. Int. J. Intelligent Systems 32, 31-50, 2017.
Fn <- function(n, x, w) { out <- 0.0 for(i in 1:n) out<- out+x[i]*w[i]; #print(out) return(out) } n <- 4 example <- wowa.weightedf(c(0.3,0.4,0.8,0.2), c(0.3,0.25,0.3,0.15), c(0.4,0.35,0.2,0.05), n, Fn, 10) exampleFn <- function(n, x, w) { out <- 0.0 for(i in 1:n) out<- out+x[i]*w[i]; #print(out) return(out) } n <- 4 example <- wowa.weightedf(c(0.3,0.4,0.8,0.2), c(0.3,0.25,0.3,0.15), c(0.4,0.35,0.2,0.05), n, Fn, 10) example
Function for calculating the value of the quantifier-based WOWA function
wowa.weightedOWAQuantifier(x, p, w, n, spl)wowa.weightedOWAQuantifier(x, p, w, n, spl)
x |
The vector of inputs |
p |
The weights of inputs x |
w |
The OWA weightings vector |
n |
The dimension of the array x |
spl |
A structure that keeps the spline knots and coefficients computed in weightedOWAQuantifierBuild function |
output |
The output is quantifier-based WOWA value |
Gleb Beliakov, Daniela L. Calderon, Deakin University
[1]G. Beliakov, H. Bustince, and T. Calvo. A Practical Guide to Averaging Functions. Springer, Berlin, Heidelberg, 2016.
[2]G. Beliakov. A method of introducing weights into OWA operators and other symmetric functions. In V. Kreinovich, editor, Uncertainty Modeling. Dedicated to B. Kovalerchuk, pages 37-52. Springer, Cham, 2017.
[3]G. Beliakov. Comparing apples and oranges: The weighted OWA function, Int.J. Intelligent Systems, 33, 1089-1108, 2018.
[4]V. Torra. The weighted OWA operator. Int. J. Intelligent Systems, 12:153-166, 1997.
[5]G. Beliakov and J.J. Dujmovic , Extension of bivariate means to weighted means of several arguments by using binary trees, Information sciences, 331, 137-147, 2016.
[6] J.J. Dujmovic and G. Beliakov. Idempotent weighted aggregation based on binary aggregation trees. Int. J. Intelligent Systems 32, 31-50, 2017.
n <- 4 pweights=c(0.3,0.25,0.3,0.15); wweights=c(0.4,0.35,0.2,0.05); tempspline <- wowa.weightedOWAQuantifierBuild(pweights,wweights , n) wowa.weightedOWAQuantifier(c(0.3,0.4,0.8,0.2), pweights, wweights, n, tempspline)n <- 4 pweights=c(0.3,0.25,0.3,0.15); wweights=c(0.4,0.35,0.2,0.05); tempspline <- wowa.weightedOWAQuantifierBuild(pweights,wweights , n) wowa.weightedOWAQuantifier(c(0.3,0.4,0.8,0.2), pweights, wweights, n, tempspline)
Function for building the RIM quantifier of the Weighted OWA function
wowa.weightedOWAQuantifierBuild(p, w, n)wowa.weightedOWAQuantifierBuild(p, w, n)
p |
The weights of inputs x |
w |
The OWA weightings vector |
n |
The dimension of the vectors p,w |
output |
A structure which has fields: spl, which keeps the spline knots and coefficients for later use in weightedOWAQuantifier, and Tnum, the number of knots in the monotone spline |
Gleb Beliakov, Daniela L. Calderon, Deakin University
[1]G. Beliakov, H. Bustince, and T. Calvo. A Practical Guide to Averaging Functions. Springer, Berlin, Heidelberg, 2016.
[2]G. Beliakov. A method of introducing weights into OWA operators and other symmetric functions. In V. Kreinovich, editor, Uncertainty Modeling. Dedicated to B. Kovalerchuk, pages 37-52. Springer, Cham, 2017.
[3]G. Beliakov. Comparing apples and oranges: The weighted OWA function, Int.J. Intelligent Systems, 33, 1089-1108, 2018.
[4]V. Torra. The weighted OWA operator. Int. J. Intelligent Systems, 12:153-166, 1997.
[5]G. Beliakov and J.J. Dujmovic , Extension of bivariate means to weighted means of several arguments by using binary trees, Information sciences, 331, 137-147, 2016.
[6] J.J. Dujmovic and G. Beliakov. Idempotent weighted aggregation based on binary aggregation trees. Int. J. Intelligent Systems 32, 31-50, 2017.
n <- 4 pweights=c(0.3,0.25,0.3,0.15); wweights=c(0.4,0.35,0.2,0.05); tspline <- wowa.weightedOWAQuantifierBuild(pweights,wweights , n) wowa.weightedOWAQuantifier(c(0.3,0.4,0.8,0.2), pweights, wweights, n, tspline)n <- 4 pweights=c(0.3,0.25,0.3,0.15); wweights=c(0.4,0.35,0.2,0.05); tspline <- wowa.weightedOWAQuantifierBuild(pweights,wweights , n) wowa.weightedOWAQuantifier(c(0.3,0.4,0.8,0.2), pweights, wweights, n, tspline)