wowa.WAn {wowa}

Extension of binary averaging

Description

Function for calculating a binary tree multivariate extension of a binary averaging function

Usage

  wowa.WAn(x, w, n, Fn, L)

Arguments

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)

Value

output

The output is Weighted n-variate mean extending Fn

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( 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