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...

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...

A method for consensus measuring in a group decision problem is presented for the multiple criteria case. The decision process is supposed to be carried out according to Saaty's Analytic Hierarchy Process, and hence using pairwise comparison among the alternatives. Using a suitable distance...

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...

We show that the incompatibility between the Pareto principle and the notion of non-discrimination as presented in Xu (2000) continues to hold when the individuals have exact preferences and the social preference relation is allowed to be a reflexive and transitive fuzzy binary relation. Our...

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...

In outranking methods for Multiple Criteria Decision Making (MCDM), pair-wise comparisons of alternatives are often summarized through a fuzzy preference relation. In this paper, the binary preference relation is extended to pairs of subsets of alternatives in order to define on this basis a...

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...