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.

Fuzzy set theory has been explicitly introduced to deal with vagueness and ambiguity. One can also use probability theory or techniques borrowed from philosophical logic. In this chapter, we consider fuzzy preferences and we survey the literature on aggregation of fuzzy preferences. We restrict...

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...

In recent works, we have proposed a graphical model to represent linguistic preferences called LCP-nets. LCP-nets have been implemented and used in a specific use case of industrial engineering. In this paper, we consolidate this contribution in formalising it through a set of notations and...

Fuzzy set theory has been explicitly introduced to deal with vagueness and ambiguity. One can also use probability theory or techniques borrowed from philosophical logic. In this chapter, we consider fuzzy preferences and we survey the literature on aggregation of fuzzy preferences. We restrict...

In a binary choice voting scenario, voters may have fuzzy preferences but are required to make crisp choices. In order to compare a crisp voting procedure with more general mechanisms of fuzzy preference aggregation, we first focus on the latter. We present a formulation of strategy-proofness in...