In this paper, we prove a fuzzy version of Arrow's Theorem that contains the crisp version. We show that under our definitions, Arrow's Theorem remains intact even if levels of intensities of the players and levels of membership in the set of alternatives are considered.

Under certain aggregation rules, particular subsets of the voting population fully characterize the social preference relation, and the preferences of the remaining voters become irrelevant. In the traditional literature, these types of rules, i.e. voting and simple rules, have received...

This paper presents the first part of a general study of the structure of nine preference-based choice functions introduced by Barrett et al.2 More precisely, we show that, as for crisp total pre-orders, first and last alternatives exist in a finite set of alternatives equipped with a strongly...