On lattice consensus methods |
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Authors: | Dean A Neumann Victor T Norton Jr |
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Institution: | (1) Department of Mathematics and Statistics, Bowling Green State University, 43403 Bowling Green, Ohio, USA |
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Abstract: | We investigate the consensus problem for classifications of three types: partitions, dendrograms, and n-trees For partitions or dendrograms, lattice polynomials define natural consensus functions We extend these lattice methods to n-trees, introducing a general class of consensus functions that includes the intersection consensus functions in current use These lattice consensus methods have a number of desirable mathematical properties We prove that they all satisfy the Pareto Axiom For each of the three classification types, we determine which lattice consensus functions satisfy the Betweenness AxiomAuthor partially supported by a research grant from the Faculty Research Committee, Bowling State University |
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Keywords: | Consensus function Lattice polynomial Partition Dendrogram n-tree Betweenness Axiom Pareto Axiom |
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