wowa.weightedf {wowa}

Weighted extension of the OWA function

Description

Function for extending order weigted averages and other multivariate symmetric functions

Usage

  wowa.weightedf(x, p, w, n, Fn, L)

Arguments

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)

Value

output

The output is the weighted ordered weigted average.

Author(s)

Gleb Beliakov, Daniela L. Calderon, Deakin University

References

[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.

Examples

  
      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)
	example