A CONSIDERATION OF DIFFERENT DEFINITIONS OF FUZZY COVERING RELATIONS

John N. Mordeson (), Terry D. Clark (), Michael B. Gibilisco () and Peter C. Casey ()
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John N. Mordeson: Department of Mathematics, Creighton University, Omaha, Nebraska 68178, USA
Terry D. Clark: Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA
Michael B. Gibilisco: Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA
Peter C. Casey: Department of Political Science, Creighton University, Omaha, Nebraska 68178, USA

New Mathematics and Natural Computation (NMNC), 2010, vol. 06, issue 03, 247-259

Abstract: Fuzzy spatial models map a substantial degree of preference indifference. It has been shown that different definitions of covering result in different elements in the uncovered set when preference indifference is present. We consider several of the most frequently used definitions of covering relations found in the literature. The first definition that we examine yields an uncovered set, some of the elements of which are not Pareto efficient. Given that there is no reason to expect a set of players comprising a majority to settle for a Pareto deficient outcome, the remainder of the paper considers the ability of alternative definitions to avoid such a result.

Keywords: Spatial models; covering relations; Pareto set; lattice; partial order; minimal generating set (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S1793005710001736

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