Metrics on partially ordered sets - A survey

Summary

More or less recent results on metrics associated with valuations or (and) minimum weighted paths in posets, metric characterizations of posets and some applications of these results to problems involving uses of distances in social sciences are reviewed.

Keywords

Mathematics, Metric (unit), Metric space, Combinatorics, Point (geometry)

References

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Cited by

Singular Points and an Upper Bound of Medians in Upper Semimodular LatticesJinlu Li, Kaddour Boukaabar — 2000
A semantic framework for multimedia document adaptationJérôme Euzenat, Nabil Layaïda, Victor Dias — 2003
Data Mining Patterns: New Methods and ApplicationsPascal Poncelet, Florent Masséglia, Maguelonne Teisseire — 2007
Rough Isometries of Order Lattices and GroupsAndreas Lochmann — 2009
Measuring the Structural Preservation of Semantic Hierarchy AlignmentCliff Joslyn, Patrick Paulson, Amanda White — 2009
Metric incremental clustering of nominal dataDan A. Simovici, Natima Singla, Michael Kuperberg — 2004
On distances and metrics in discrete ordered setsStephan Foldes, Sándor Radeleczki — 2020
QUADRUPLE FIXED POINT THEOREMS FOR (α,ψ) - CONTRACTIVE TYPE MAPPINGS IN PARTIALLY ORDERED METRIC SPACESManoj Ughade, P. L. Sanodia, Arvind Gupta — 2015
Meir-Keeler Type n-tuplet Fixed Point Theorems in Partially Ordered Metric SpacesManoj Ughade, R. D. Daheriya — 2014
Tripled Fixed Point Results in Generalized Metric Spaces under Nonlinear Type Contractions Depended on another FunctionManoj Ughade, R. D. Daheriya — 2015
An Algebraic Approach to Inductive LearningZdravko Markov — 2000
Irreducible Elements in Metric LatticesAndreas Lochmann — 2010
Valuations and Metrics on Partially Ordered SetsChris Orum, Cliff Joslyn — 2009
Valuations and closure operators on finite latticesLéonard Kwuida, Stefan E. Schmidt — 2011
Lattice valuations, medians and majoritiesBruno Leclerc — 1993
Two Shortest Path Metrics on Well-Formed Parentheses StringsChristian Germain, Jean Marcel Pallo — 1996
Comparison of classifications using measures intermediate between metric dissimilarity and consensus similarityDaniel P. Faith, Lee Belbin — 1986
On the Rotation Distance in the Lattice of Binary TreesJean Marcel Pallo — 1987
On pruning the search space for clustering ensemble problemsSandro Vega-Pons, Paolo Avesani — 2015
Distributions of Tree Comparison Metrics—Some New ResultsMike Steel, David Penny — 1993

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