Axioms for Consensus Functions on the n-Cube. (9th January 2017)

• Record Type: Journal Article
• Authors: Garcia-Martinez, C.; McMorris, F. R.; Ortega, O.; Powers, R. C.
• Other Names: Fotakis Dimitris Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2017(2017)
• Publication Date: 2017-01-09
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2017/8025616
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : A p value of a sequence π = ( x 1, x 2, …, x k ) of elements of a finite metric space ( X, d ) is an element x for which ∑ i = 1 k d p ( x, x i ) is minimum. The l p –function with domain the set of all finite sequences on X and defined by l p ( π ) = { x : x is a p value of π } is called the l p –function on ( X, d ) . The l 1 and l 2 functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of the l p –functions on the n -cube are given. In addition, the center function (using the minimax criterion) is characterized as well as new results proved for the median and antimedian functions.