The uncovered set and indifference in spatial models: A fuzzy set approach

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https://www.sciencedirect.com/science/article/abs/pii/S0165011410004471#!

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https://doi.org/10.1016/j.fss.2010.10.016
 http://hdl.handle.net/11603/20950

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2010-11-09

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journal articles preprints
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Mordeson, John N.; Clark, Terry D.; Miller, Nicholas R.; Casey, Peter C.; Gibilisco, Michael B.; The uncovered set and indifference in spatial models: A fuzzy set approach; Fuzzy Sets and Systems, Volume 168, Issue 1, Pages 89-101 (2010); https://www.sciencedirect.com/science/article/abs/pii/S0165011410004471#!

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© 2010 Elsevier B.V. All rights reserved.

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Abstract

The uncovered set was developed in order to predict outcomes when spatial models result in an empty core. In contrast to conventional approaches, fuzzy spatial models induce a substantial degree of individual and collective indifference over alternatives. Hence, existing definitions of the covering relationship return differing results. We develop a definition for a fuzzy covering relation. Our definition results in an uncovered set that is, in most cases, contained within the Pareto set. We conclude by characterizing the exceptions.