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

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.