2006•International Journal of Uncertainty Fuzziness and Knowledge-Based SystemsRequires access

A NOTE ON FAIR DIVISION UNDER INTERVAL UNCERTAINTY

Gerhard J. Woeginger

Abstract

In a recent paper [International Journal of Uncertainty, Fuzziness, and Knowledge-Based Systems 8:611–618], Yager & Kreinovich characterize a certain proportional division rule in terms of the three axioms (1) symmetry, (2) participant mergability, and (3) continuity. This technical note tightens their characterization: The proportional division rule is already fully characterized by the first two axioms (1) symmetry and (2) participant mergability.

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Key concepts: Axiom, Division (mathematics), Interval (graph theory), Symmetry (geometry), Mathematical economics, Characterization (materials science), Mathematics, Calculus (dental)