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2017 Axioms for Consensus Functions on the n-Cube
C. Garcia-Martinez, F. R. McMorris, O. Ortega, R. C. Powers
J. Appl. Math. 2017: 1-5 (2017). DOI: 10.1155/2017/8025616

Abstract

A p value of a sequence π=(x1,x2,,xk) of elements of a finite metric space (X,d) is an element x for which i=1kdp(x,xi) is minimum. The lp–function with domain the set of all finite sequences on X and defined by lp(π)={x:x is a p value of π} is called the lp–function on (X,d). The l1 and l2 functions are the well-studied median and mean functions, respectively. In this note, simple characterizations of the lp–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.

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C. Garcia-Martinez. F. R. McMorris. O. Ortega. R. C. Powers. "Axioms for Consensus Functions on the n-Cube." J. Appl. Math. 2017 1 - 5, 2017. https://doi.org/10.1155/2017/8025616

Information

Received: 30 June 2016; Accepted: 6 December 2016; Published: 2017
First available in Project Euclid: 24 February 2017

zbMATH: 07037491
MathSciNet: MR3599835
Digital Object Identifier: 10.1155/2017/8025616

Rights: Copyright © 2017 Hindawi

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