TY - JOUR
T1 - The uncovered set and indifference in spatial models
T2 - A fuzzy set approach
AU - Mordeson, John N.
AU - Clark, Terry D.
AU - Miller, Nicholas R.
AU - Casey, Peter C.
AU - Gibilisco, Michael B.
N1 - Funding Information:
This article is a revised version of a paper presented at the 2009 annual conference of the Public Choice Society. We thank the anonymous reviewers and editorial staff of Fuzzy Sets and Systems for their invaluable assistance in improving this manuscript. We owe a special debt of gratitude to Lotfi Zadeh, George Klir, and Paul Wang for their encouragement and support of the fuzzy spatial modeling project, of which the research reported in this article is a part. We also wish to express our appreciation to Jay Verkuilen and Joseph Godfrey for their substantive comments on previous versions of this manuscript, Anne Bautch for the many hours she spent designing and solving amendment agendas, and Adam Karnik for helping us to work through the effect of indifference on covering relations. Finally, we gratefully acknowledge the funding provided by an Academic Affairs Research Initiative Grant, the Center for Mathematics of Uncertainty, and the College of Arts and Sciences at Creighton University.
PY - 2011/4/1
Y1 - 2011/4/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.fss.2010.10.016
DO - 10.1016/j.fss.2010.10.016
M3 - Article
AN - SCOPUS:79551525395
VL - 168
SP - 89
EP - 101
JO - Fuzzy Sets and Systems
JF - Fuzzy Sets and Systems
SN - 0165-0114
IS - 1
ER -