Utility function of fuzzy preferences on a countable set under max-*-transitivity

Countable set, Fuzzy binary relation, Max-*-transitivity, Utility function,

A modal account of preference in a fuzzy setting

In this paper we first consider the problem of extending fuzzy (weak and strict) preference relations, represented by fuzzy preorders on a set to a fuzzy preferences on subsets, and we characterise different possibilities. Based on their properties, we then semantically define and axiomatize several two-tiered graded modal logics to reason about the corresponding different notions of fuzzy preferences.Esteva and Godo acknowledges partial support by the Spanish FEDER/MINECO project TIN2015-71799-C2-1-P. Vidal acknowledges partial support by the joint project of the Austrian Science Fund (FWF) I1897-N25 and the Czech Science Foundation (GACR) 15-34650L, and by the institutional grant RVO:67985807.Peer reviewe